{"input": "A rock is thrown vertically upward with initial speed $v_{0}$. Assume a friction force proportional to $-v$, where $v$ is the velocity of the rock, and neglect the buoyant force exerted by air. Which of the following is correct?\n\nA. The acceleration of the rock is always equal to $\\mathbf{g}$.\n\nB. The acceleration of the rock is equal to $\\mathrm{g}$ only at the top of the flight.\n\nC. The acceleration of the rock is always less than $g$.\n\nD. The speed of the rock upon return to its starting point is $v_{0}$.\n\nE. The rock can attain a terminal speed greater than $v_{0}$ before it returns to its starting point.\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A satellite orbits the Earth in a circular orbit. An astronaut on board perturbs the orbit slightly by briefly firing a control jet aimed toward the Earth's center. Afterward, which of the following is true of the satellite's path?\n\nA. It is an ellipse.\n\nB. It is a hyperbola.\n\nC. It is a circle with larger radius.\n\nD. It is a spiral with increasing radius.\n\nE. It exhibits many radial oscillations per revolution.\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "For blue light, a transparent material has a relative permittivity (dielectric constant) of 2.1 and a relative permeability of 1.0 . If the speed of light in a vacuum is $c$, the phase velocity of blue light in an unbounded medium of this material is\n\nA. $\\sqrt{3.1} c$\n\nB. $\\sqrt{2.1} c$\n\nC. $\\frac{c}{\\sqrt{1.1}}$\n\nD. $\\frac{c}{\\sqrt{2.1}}$\n\nE. $\\frac{c}{\\sqrt{3.1}}$", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "The equation $y=A \\sin 2 \\pi\\left(\\frac{t}{T}-\\frac{x}{\\lambda}\\right)$, where $A, T$, and $\\lambda$ are positive constants, represents a wave whose\n\nA. amplitude is $2 \\mathrm{~A}$\n\nB. velocity is in the negative $x$-direction\n\nC. period is $\\frac{T}{\\lambda}$\n\nD. speed is $\\frac{x}{t}$\n\nE. speed is $\\frac{\\lambda}{T}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "Two small spheres of putty, $A$ and $B$, of mass $M$ and $3 M$, respectively, hang from the ceiling on strings of equal length $\\ell$. Sphere $A$ is drawn aside so that it is raised to a height $h_{0}$ as shown above and then released. Sphere $A$ collides with sphere $B$; they stick together and swing to a maximum height $h$ equal to\nA. $\\frac{1}{16} h_{0}$\nB. $\\frac{1}{8} h_{0}$\nC. $\\frac{1}{4} h_{0}$\nD. $\\frac{1}{3} h_{0}$\nE. $\\frac{1}{2} h_{0}$\n\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "A particle is initially at rest at the top of a curved frictionless track. The $x$ - and $y$-coordinates of the track are related in dimensionless units by $y=\\frac{x^{2}}{4}$, where the positive $y$-axis is in the vertical downward direction. As the particle slides down the track, what is its tangential acceleration?\n\nA. 0\n\nB. $g$\n\nC. $\\frac{g x}{2}$\n\nD. $\\frac{g x}{\\sqrt{x^{2}+4}}$\n\nE. $\\frac{g x^{2}}{\\sqrt{x^{2}+16}}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": true}
{"input": "A 2-kilogram box hangs by a massless rope from a ceiling. A force slowly pulls the box horizontally to the side until the horizontal force is 10 newtons. The box is then in equilibrium as shown above. The angle that the rope makes with the vertical is closest to\n\nA. $\\arctan 0.5$\n\nB. $\\arcsin 0.5$\n\nC. $\\arctan 2.0$\n\nD. $\\arcsin 2.0$\n\nE. $45^{\\circ}$", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "A 5-kilogram stone is dropped on a nail and drives the nail 0.025 meter into a piece of wood. If the stone is moving at 10 meters per second when it hits the nail, the average force exerted on the nail by the stone while the nail is going into the wood is most nearly\n\nA. 10 N \n\nB. 100 N \n\nC. 1000 N \n\nD. 10,000 N \n\nE. 100,000 N ", "has_image": false}
{"input": "A wire of diameter 0.02 meter contains $1 \\times 10^{28}$ free electrons per cubic meter. For an electric current of 100 amperes, the drift velocity for free electrons in the wire is most nearly\n\nA. $0.6 \\times 10^{-29} \\mathrm{~m} / \\mathrm{s}$\n\nB. $1 \\times 10^{-19} \\mathrm{~m} / \\mathrm{s}$\n\nC. $5 \\times 10^{-10} \\mathrm{~m} / \\mathrm{s}$\n\nD. $2 \\times 10^{-4} \\mathrm{~m} / \\mathrm{s}$\n\nE. $8 \\times 10^{3} \\mathrm{~m} / \\mathrm{s}$\n\nElectric Field\n\nMagnitude\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "An isolated sphere of radius $R$ contains a uniform volume distribution of positive charge. Which of the curves on the graph above correctly illustrates the dependence of the magnitude of the electric field of the sphere as a function of the distance $r$ from its center?\nA. $A$\nB. $B$\nC. $C$\nD. $D$\nE. $E$\n\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": true}
{"input": "Which of the following equations is a consequence of the equation $\\nabla \\times \\mathbf{H}=\\dot{\\mathbf{D}}+\\mathbf{J}$ ?\n\nA. $\\nabla \\cdot(\\dot{\\mathbf{D}}+\\mathbf{J})=0$\n\nB. $\\nabla \\times(\\dot{\\mathbf{D}}+\\mathbf{J})=0$\n\nC. $\\nabla(\\dot{\\mathbf{D}} \\cdot \\mathbf{J})=0$\n\nD. $\\dot{\\mathbf{D}}+\\mathrm{J}=0$\n\nE. $\\dot{\\mathbf{D}} \\cdot \\mathbf{J}=\\mathbf{0}$\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A source of 1-kilohertz sound is moving straight toward you at a speed 0.9 times the speed of sound. The frequency you receive is\n\nA. $0.1 \\mathrm{kHz}$\n\nB. $0.5 \\mathrm{kHz}$\n\nC. $1.1 \\mathrm{kHz}$\n\nD. $1.9 \\mathrm{kHz}$\n\nE. $10 \\mathrm{kHz}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "Two coherent sources of visible monochromatic light form an interference pattern on a screen. If the relative phase of the sources is varied from 0 to $2 \\pi$ at a frequency of 500 hertz, which of the following best describes the effect, if any, on the interference pattern?\n\nA. It is unaffected because the frequency of the phase change is very small compared to the frequency of visible light.\n\nB. It is unaffected because the frequency of the phase change is an integral multiple of $\\pi$.\n\nC. It is destroyed except when the phase difference is 0 or $\\pi$.\n\nD. It is destroyed for all phase differences because the monochromaticity of the sources is destroyed.\n\nE. It is not destroyed but simply shifts positions at a rate too rapid to be detected by the eye.", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "For an ideal gas, the specific heat at constant pressure $C_{p}$ is greater than the specific heat at constant volume $C_{\\nu}$ because the\n\nA. gas does work on its environment when its pressure remains constant while its temperature is increased\n\nB. heat input per degree increase in temperature is the same in processes for which either the pressure or the volume is kept constant\n\nC. pressure of the gas remains constant when its temperature remains constant\n\nD. increase in the gas's internal energy is greater when the pressure remains constant than when the volume remains constant\n\nE. heat needed is greater when the volume remains constant than when the pressure remains constant\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A sample of $N$ atoms of helium gas is confined in a 1.0 cubic meter volume. The probability that none of the helium atoms is in a $1.0 \\times 10^{-6}$ cubic meter volume of the container is\nA. 0\nB. $\\left(10^{-6}\\right)^{N}$\nC. $\\left(1-10^{-6}\\right)^{N}$\nD. $1-\\left(10^{-6}\\right)^{N}$\nE. 1\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "Except for mass, the properties of the muon most closely resemble the properties of the\nA. electron\nB. graviton\nC. photon\nD. pion\nE. proton\n\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "Suppose that ${ }_{Z}^{A} X$ decays by natural radioactivity in two stages to ${ }_{Z-1}^{A-4} Y$. The two stages would most likely be which of the following?\n$\\underline{\\text { First Stage }}$\n$\\underline{\\text { Second Stage }}$\nA. $\\beta^{-}$emission with an antineutrino\n$\\alpha$ emission\nB. $\\boldsymbol{\\beta}^{-}$emission\n$\\alpha$ emission with a neutrino\nC. $\\boldsymbol{\\beta}^{-}$emission\n$\\gamma$ emission\nD. Emission of a deuteron Emission of two neutrons\nE. $\\alpha$ emission $\\gamma$ emission\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "The wave function $\\psi(x)=A \\exp \\left\\{-\\frac{b^{2} x^{2}}{2}\\right\\}$, where $A$ and $b$ are real constants, is a normalized eigenfunction of the Schrödinger equation for a particle of mass $M$ and energy $E$ in a one dimensional potential $V(x)$ such that $V(x)=0$ at $x=0$. Which of the following is correct?\n\nA. $V=\\frac{\\hbar^{2} b^{4}}{2 M}$\n\nB. $V=\\frac{\\hbar^{2} b^{4} x^{2}}{2 M}$\n\nC. $V=\\frac{\\hbar^{2} b^{6} x^{4}}{2 M}$\n\nD. $E=\\hbar^{2} b^{2}\\left(1-b^{2} x^{2}\\right)$\n\nE. $E=\\frac{\\hbar^{2} b^{4}}{2 M}$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "The energy levels of the hydrogen atom are given in terms of the principal quantum number $n$ and a positive constant $A$ by the expression\n\nA. $A\\left(n+\\frac{1}{2}\\right)$\n\nB. $A\\left(1-n^{2}\\right)$\n\nC. $A\\left(-\\frac{1}{4}+\\frac{1}{n^{2}}\\right)$\n\nD. $A n^{2}$\n\nE. $-\\frac{A}{n^{2}}$", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "A positive kaon $\\left(K^{+}\\right)$has a rest mass of $494 \\mathrm{MeV} / c^{2}$, whereas a proton has a rest mass of $938 \\mathrm{MeV} / c^{2}$. If a kaon has a total energy that is equal to the proton rest energy, the speed of the kaon is most nearly\n\nA. $0.25 c$\n\nB. $0.40 c$\n\nC. $0.55 c$\n\nD. $0.70 c$\n\nE. $0.85 c$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "Two observers $O$ and $O^{\\prime}$ observe two events, $A$ and $B$. The observers have a constant relative speed of $0.8 c$. In units such that the speed of light is 1 , observer $O$ obtained the following coordinates:\n\nEvent $A: x=3, y=3, z=3, t=3$\n\nEvent $B: x=5, y=3, z=1, t=5$\n\nWhat is the length of the space-time interval between these two events, as measured by $O^{\\prime}$ ?\nA. 1\nB. $\\sqrt{2}$\nC. 2\nD. 3\nE. $2 \\sqrt{3}$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "Which of the following statements most accurately describes how an electromagnetic field behaves under a Lorentz transformation?\n\nA. The electric field transforms completely into a magnetic field.\n\nB. If initially there is only an electric field, after the transformation there may be both an electric and a magnetic field.\n\nC. The electric field is unaltered.\n\nD. The magnetic field is unaltered.\n\nE. It cannot be determined unless a gauge transformation is also specified.\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "Which of the following statements concerning the electrical conductivities at room temperature of a pure copper sample and a pure silicon sample is NOT true?\n\nA. The conductivity of the copper sample is many orders of magnitude greater than that of the silicon sample.\n\nB. If the temperature of the copper sample is increased, its conductivity will decrease.\n\nC. If the temperature of the silicon sample is increased, its conductivity will increase.\n\nD. The addition of an impurity in the copper sample always decreases its conductivity.\n\nE. The addition of an impurity in the silicon sample always decreases its conductivity.\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "The battery in the diagram above is to be charged by the generator $G$. The generator has a terminal voltage of 120 volts when the charging current is 10 amperes. The battery has an emf of 100 volts and an internal resistance of $1 \\mathrm{ohm}$. In order to charge the battery at 10 amperes charging current, the resistance $R$ should be set at\nA. $0.1 \\Omega$\nB. $0.5 \\Omega$\nD. $5.0 \\Omega$\nE. $10.0 \\Omega$\nC. $1.0 \\Omega$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": true}
{"input": "A charged particle is released from rest in a region where there is a constant electric field and a constant magnetic field. If the two fields are parallel to each other, the path of the particle is a\n\nA. circle\n\nB. parabola\n\nC. helix\n\nD. cycloid\n\nE. straight line\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "A nickel target $(Z=28)$ is bombarded with fast electrons. The minimum electron kinetic energy needed to produce $\\mathrm{x}$-rays in the $K$ series is most nearly \n\nA. 10 eV \n\nB. 100 eV \n\nC. 1000 eV \n\nD. 10,000 eV \n\nE. 100,000 eV\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "The hypothesis that an electron possesses spin is qualitatively significant for the explanation of all of the following topics EXCEPT the\n\nA. structure of the periodic table\n\nB. specific heat of metals\n\nC. anomalous Zeeman effect\n\nD. deflection of a moving electron by a uniform magnetic field\n\nE. fine structure of atomic spectra", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "Eigenfunctions for a rigid dumbbell rotating about its center have a $\\phi$ dependence of the form $\\psi(\\phi)=A e^{i m \\phi}$, where $m$ is a quantum number and $A$ is a constant. Which of the following values of $A$ will properly normalize the eigenfunction?\n\nA. $\\sqrt{2 \\pi}$\n\nB. $2 \\pi$\n\nC. $(2 \\pi)^{2}$\n\nD. $\\frac{1}{\\sqrt{2 \\pi}}$\n\nE. $\\frac{1}{2 \\pi}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "A negative test charge is moving near a long straight wire in which there is a current. A force will act on the test charge in a direction parallel to the direction of the current if the motion of the charge is in a direction\n\nA. toward the wire\n\nB. away from the wire\n\nC. the same as that of the current\n\nD. opposite to that of the current\n\nE. perpendicular to both the direction of the current and the direction toward the wire\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "The configuration of the potassium atom in its ground state is $1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{1}$. Which of the following statements about potassium is true?\n\nA. Its $n=3$ shell is completely filled.\n\nB. Its $4 s$ subshell is completely filled.\n\nC. Its least tightly bound electron has $\\ell=4$.\n\nD. Its atomic number is 17.\n\nE. Its electron charge distribution is spherically symmetrical.\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "When the photoelectric equation is satisfied and applicable to this situation, $V$ is the\n\nA. negative value at which the current stops\n\nB. negative value at which the current starts\n\nC. positive value at which the current stops\n\nD. positive value at which the current starts\n\nE. voltage induced when the light is on", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "The photoelectric equation is derived under the assumption that\n\nA. electrons are restricted to orbits of angular momentum $n \\hbar$, where $n$ is an integer\n\nB. electrons are associated with waves of wavelength $\\lambda=h / p$, where $p$ is momentum\n\nC. light is emitted only when electrons jump between orbits\n\nD. light is absorbed in quanta of energy $E=h \\nu$\n\nE. light behaves like a wave\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "The quantity $W$ in the photoelectric equation is the\n\nA. energy difference between the two lowest electron orbits in the atoms of the photocathode\n\nB. total light energy absorbed by the photocathode during the measurement\n\nC. minimum energy a photon must have in order to be absorbed by the photocathode\n\nD. minimum energy required to free an electron from its binding to the cathode material\n\nE. average energy of all electrons in the photocathode\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "The potential energy of a body constrained to move on a straight line is $k x^{4}$ where $k$ is a constant. The position of the body is $x$, its speed $v$, its linear momentum $p$, and its mass $m$.\n\nThe force on the body is\nA. $\\frac{1}{2} m v^{2}$\nB. $-4 k x^{3}$\nC. $k x^{4}$\nD. $-\\frac{k x^{5}}{5}$\nE. $m g$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "The potential energy of a body constrained to move on a straight line is $k x^{4}$ where $k$ is a constant. The position of the body is $x$, its speed $v$, its linear momentum $p$, and its mass $m$.\n\nThe Hamiltonian function for this system is\nA. $\\frac{p^{2}}{2 m}+k x^{4}$\nB. $\\frac{p^{2}}{2 m}-k x^{4}$\nC. $k x^{4}$\nD. $\\frac{1}{2} m v^{2}-k x^{4}$\nE. $\\frac{1}{2} m v^{2}$\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "The potential energy of a body constrained to move on a straight line is $k x^{4}$ where $k$ is a constant. The position of the body is $x$, its speed $v$, its linear momentum $p$, and its mass $m$.\n\nThe body moves from $x_{1}$ at time $t_{1}$ to $x_{2}$ at time $t_{2}$. Which of the following quantities is an extremum for the $x-t$ curve corresponding to this motion, if end points are fixed?\n\nA. $\\int_{t_{1}}^{t_{2}}\\left(\\frac{1}{2} m v^{2}-k x^{4}\\right) d t$\n\nB. $\\int_{t_{1}}^{t_{2}}\\left(\\frac{1}{2} m v^{2}\\right) d t$\n\nC. $\\int_{t_{1}}^{t_{2}}(m x v) d t$\n\nD. $\\int_{x_{1}}^{x_{2}}\\left(\\frac{1}{2} m v^{2}+k x^{4}\\right) d x$\n\nE. $\\int_{x_{1}}^{x_{2}}(m v) d x$\n\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "The figure above represents a point mass $m$ attached to the ceiling by a cord of fixed length $\\ell$. If the point mass moves in a horizontal circle of radius $r$ with uniform angular velocity $\\omega$, the tension in the cord is\n\nA. $m g\\left(\\frac{r}{\\ell}\\right)$\n\nB. $m g \\cos \\left(\\frac{\\theta}{2}\\right)$\n\nC. $\\frac{m \\omega r}{\\sin \\left(\\frac{\\theta}{2}\\right)}$\n\nD. $m\\left(\\omega^{2} r^{2}+g^{2}\\right)^{\\frac{1}{2}}$\n\nE. $m\\left(\\omega^{4} r^{2}+g^{2}\\right)^{\\frac{1}{2}}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "If logical 0 is 0 volts and logical 1 is +1 volt, the circuit shown above is a logic circuit commonly known as\n\nA. an OR gate\n\nB. an AND gate\n\nC. a 2-bit adder\n\nD. a flip-flop\n\nE. a fanout\n\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "The gain of an amplifier is plotted versus angular frequency $\\omega$ in the diagram above. If $K$ and $a$ are positive constants, the frequency dependence of the gain near $\\omega=3 \\times 10^{5}$ second $^{-1}$ is most accurately expressed by\nA. $K e^{-a \\omega}$\nB. $K \\omega^{2}$\nC. $K \\omega$\nD. $K \\omega^{-1}$\nE. $K \\omega^{-2}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "An experimenter measures 9934 counts during one hour from a radioactive sample. From this number the counting rate of the sample can be estimated with a standard deviation of most nearly\nA. 100\nB. 200\nC. 300\nD. 400\nE. 500\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "Which of the following nuclei has the largest binding energy per nucleon? (Consider the most abundant isotope of each element.)\n\nA. Helium\n\nB. Carbon\n\nC. Iron\n\nD. Uranium\n\nE. Plutonium\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "A proton beam is incident on a scatterer 0.1 centimeter thick. The scatterer contains $10^{20}$ target nuclei per cubic centimeter. In passing through the scatterer, one proton per incident million is scattered. The scattering cross section is\n\nA. $10^{-29} \\mathrm{~cm}^{2}$\n\nB. $10^{-27} \\mathrm{~cm}^{2}$\n\nC. $10^{-25} \\mathrm{~cm}^{2}$\n\nD. $10^{-23} \\mathrm{~cm}^{2}$\n\nE. $10^{-21} \\mathrm{~cm}^{2}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "Three masses are connected by two springs as shown above. A longitudinal normal mode with frequency $\\frac{1}{2 \\pi} \\sqrt{\\frac{k}{m}}$ is exhibited by\n\nA. $A, B, C$ all moving in the same direction with equal amplitude\n\nB. $A$ and $C$ moving in opposite directions with equal amplitude, and $B$ at rest\n\nC. $A$ and $C$ moving in the same direction with equal amplitude, and $B$ moving in the opposite direction with the same amplitude\n\nD. $A$ and $C$ moving in the same direction with equal amplitude, and $B$ moving in the opposite direction with twice the amplitude\n\nE. none of the above\n\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "A uniform stick of length $L$ and mass $M$ lies on a frictionless horizontal surface. A point particle of mass $\\boldsymbol{m}$ approaches the stick with speed $v$ on a straight line perpendicular to the stick that intersects the stick at one end, as shown above. After the collision, which is elastic, the particle is at rest. The speed $V$ of the center of mass of the stick after the collision is\nA. $\\frac{m}{M} v$\nB. $\\frac{m}{M+m} v$\nC. $\\sqrt{\\frac{m}{M}} v$\nD.<smiles>[Y14]1=CCC2CCCC1C2</smiles>\nE. $\\frac{3 m}{\\bar{M}} v$\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "Photons of wavelength $\\lambda$ scatter elastically on free protons initially at rest. The wavelength of the photons scattered at $90^{\\circ}$ is increased by\n\nA. $\\lambda / 137$\n\nB. $\\lambda / 1836$\n\nC. $h / m_{e} c$, where $h$ is Planck's constant, $m_{e}$ the rest mass of an electron, and $c$ the speed of light\n\nD. $h / m_{p} c$, where $h$ is Planck's constant, $m_{p}$ the rest mass of a proton, and $c$ the speed of light\n\nE. zero\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "A blackbody at temperature $T_{1}$ radiates energy at a power level of 10 milliwatts $(\\mathrm{mW})$. The same blackbody, when at a temperature $2 T_{1}$, radiates energy at a power level of\nA. $10 \\mathrm{~mW}$\nD. $80 \\mathrm{~mW}$\nB. $20 \\mathrm{~mW}$\nC. $40 \\mathrm{~mW}$\nE. $160 \\mathrm{~mW}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "The Franck-Hertz experiment and related scattering experiments show that\n\nA. electrons are always scattered elastically from atoms\n\nB. electrons are never scattered elastically from atoms\n\nC. electrons of a certain energy range can be scattered inelastically, and the energy lost by electrons is discrete\n\nD. electrons always lose the same energy when they are scattered inelastically\n\nE. there is no energy range in which the energy lost by electrons varies continuously\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "A transition in which one photon is radiated by the electron in a hydrogen atom when the electron's wave function changes from $\\psi_{1}$ to $\\psi_{2}$ is forbidden if $\\psi_{1}$ and $\\psi_{2}$\n\nA. have opposite parity\n\nB. are orthogonal to each other\n\nC. are zero at the center of the atomic nucleus\n\nD. are both spherically symmetrical\n\nE. are associated with different angular momenta\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "The Hamiltonian operator in the Schrödinger equation can be formed from the classical Hamiltonian by substituting\n\nA. wavelength and frequency for momentum and energy\n\nB. a differential operator for momentum\n\nC. transition probability for potential energy\n\nD. sums over discrete eigenvalues for integrals over continuous variables\n\nE. Gaussian distributions of observables for exact values\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "The Hall effect is used in solid-state physics to measure\n\nA. ratio of charge to mass\n\nB. magnetic susceptibility\n\nC. the sign of the charge carriers\n\nD. the width of the gap between the conduction and valence bands\n\nE. Fermi energy", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "One feature common to both the Debye theory and the Einstein theory of the specific heat of a crystal composed of $N$ identical atoms is that the\n\nA. average energy of each atom is $3 k T$\n\nB. vibrational energy of the crystal is equivalent to the energy of $3 \\mathrm{~N}$ independent harmonic oscillators\n\nC. crystal is assumed to be continuous for all elastic waves\n\nD. speed of the longitudinal elastic waves is less than the speed of the transverse elastic waves\n\nE. upper cutoff frequency of the elastic waves is the same\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A cube has a constant electric potential $V$ on its surface. If there are no charges inside the cube, the potential at the center of the cube is\nA. zero\nD. $V / 2$\nB. $V / 8$\nC. $V / 6$\nE. $V$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "A charged particle oscillates harmonically along the $x$-axis as shown above. The radiation from the particle is detected at a distant point $P$, which lies in the $x y$-plane. The electric field at $P$ is in the\n\nA. $\\pm z$ direction and has a maximum amplitude at $\\theta=90^{\\circ}$\n\nB. $\\pm z$ direction and has a minimum amplitude at $\\theta=90^{\\circ}$\n\nC. $x y$-plane and has a maximum amplitude at $\\theta=90^{\\circ}$\n\nD. $x y$-plane and has a minimum amplitude at $\\theta=90^{\\circ}$\n\nE. $x y$-plane and has a maximum amplitude at $\\theta=45^{\\circ}$\n\nDielectric $K$\n\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": true}
{"input": "A dielectric of dielectric constant $K$ is placed in contact with a conductor having surface charge density $\\sigma$, as shown above. What is the polarization (bound) charge density $\\sigma_{p}$ on the surface of the dielectric at the interface between the two materials?\nA. $\\sigma \\frac{K}{1-K}$\nB. $\\sigma \\frac{K}{1+K}$\nC. $\\sigma K$\nD. $\\sigma \\frac{1+K}{K}$\nE. $\\sigma \\frac{1-K}{K}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "The mean kinetic energy of electrons in metals at room temperature is usually many times the thermal energy $k T$. Which of the following can best be used to explain this fact?\n\nA. The energy-time uncertainty relation\n\nB. The Pauli exclusion principle\n\nC. The degeneracy of the energy levels\n\nD. The Born approximation\n\nE. The wave-particle duality\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "If $\\psi$ is a normalized solution of the Schrödinger equation and $Q$ is the operator corresponding to a physical observable $x$, the quantity $\\psi * Q \\psi$ may be integrated in order to obtain the\n\nA. normalization constant for $\\psi$\n\nB. spatial overlap of $Q$ with $\\psi$\n\nC. mean value of $x$\n\nD. uncertainty in $x$\n\nE. time derivative of $x$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "Which of the following is an eigenfunction of the linear momentum operator $-i \\hbar \\frac{\\partial}{\\partial x}$ with a positive eigenvalue $\\hbar k$; i.e., an eigenfunction that describes a particle that is moving in free space in the direction of positive $x$ with a precise value of linear momentum?\nA. $\\cos k x$\nB. $\\sin k x$\nC. $\\mathrm{e}^{-i k x}$\nD. $\\mathrm{e}^{i k x}$\nE. $\\mathrm{e}^{-k x}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "In an ordinary hologram, coherent monochromatic light produces a 3 -dimensional picture because wave information is recorded for which of the following?\n\n1. Amplitude\n\nII. Phase\n\nIII. Wave-front angular frequency\n\nA. I only\n\nB. I and II only\n\nC. 1 and III only\n\nD. II and III only\n\nE. I, II, and III\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "The dispersion law for a certain type of wave motion is $\\omega=\\left(c^{2} k^{2}+m^{2}\\right)^{\\frac{1}{2}}$, where $\\omega$ is the angular frequency, $k$ is the magnitude of the propagation vector, and $c$ and $m$ are constants. The group velocity of these waves approaches\n\nA. infinity as $k \\rightarrow 0$ and zero as $k \\rightarrow \\infty$\n\nB. infinity as $k \\rightarrow 0$ and $c$ as $k \\rightarrow \\infty$\n\nC. $c$ as $k \\rightarrow 0$ and zero as $k \\rightarrow \\infty$\n\nD. zero as $k \\rightarrow 0$ and infinity as $k \\rightarrow \\infty$\n\nE. zero as $k \\rightarrow 0$ and $c$ as $k \\rightarrow \\infty$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "A particle of mass $m$ that moves along the $x$-axis has potential energy $V(x)=a+b x^{2}$, where $a$ and $b$ are positive constants. Its initial velocity is $v_{0}$ at $x=0$. It will execute simple harmonic motion with a frequency determined by the value of\n\nA. $b$ alone\n\nB. $b$ and $a$ alone\n\nC. $b$ and $m$ alone\n\nD. $b, a$, and $m$ alone\n\nE. $b, a, m$, and $v_{0}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "The equation of motion of a rocket in free space can be written\n\n$$\nm \frac{d v}{d t}+u \frac{d m}{d t}=0\n$$\n\nwhere $m$ is the rocket's mass, $v$ is its velocity, $t$ is time, and $u$ is a constant.\n\nThe constant $u$ represents the speed of the\n\nA. rocket at $t=0$\n\nB. rocket after its fuel is spent\n\nC. rocket in its instantaneous rest frame\n\nD. rocket's exhaust in a stationary frame\n\nE. rocket's exhaust relative to the rocket\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "The equation of motion of a rocket in free space can be written\n\n$$\nm \frac{d v}{d t}+u \frac{d m}{d t}=0\n$$\n\nwhere $m$ is the rocket's mass, $v$ is its velocity, $t$ is time, and $u$ is a constant.\n\nThe equation can be solved to give $v$ as a function of $m$. If the rocket has $m=m_{0}$ and $v=0$ when it starts, what is the solution?\n\nA. $u m_{0} / m$\n\nB. $u \\exp \\left(m_{0} / m\\right)$\n\nC. $u \\sin \\left(m_{0} / m\\right)$\n\nD. $u \\tan \\left(m_{0} / m\\right)$\n\nE. None of the above.\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "A point charge $-q$ coulombs is placed at a distance $d$ from a large grounded conducting plane. The surface charge density on the plane a distance $D$ from the point charge is\n\nA. $\\frac{q}{4 \\pi D}$\n\nB. $\\frac{q D^{2}}{2 \\pi}$\n\nC. $\\frac{q d}{2 \\pi D^{2}}$\n\nD. $\\frac{g d}{2 \\pi D^{3}}$\n\nE. $\\frac{q d}{4 \\pi \\epsilon_{0} D^{2}}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "An alternating current electrical generator has a fixed internal impedance $\\boldsymbol{R}_{\\boldsymbol{g}}+j X_{g}$ and is used to supply power to a passive load that has an impedance $\\boldsymbol{R}_{g}+j X_{\\ell}$, where $j=\\sqrt{-1}$, $R_{g} \\neq 0$, and $X_{g} \\neq 0$. For maximum power transfer between the generator and the load, $X_{\\ell}$ should be equal to\nA. 0\nB. $X_{g}$\nC. $-X_{g}$\nD. $\\boldsymbol{R}_{\\boldsymbol{g}}$\nE. $-\\boldsymbol{R}_{\\boldsymbol{g}}$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "A current $i$ in a circular loop of radius $b$ produces a magnetic field. At a fixed point far from the loop, the strength of the magnetic field is proportional to which of the following combinations of $i$ and $b$ ?\nA. $i b$\nB. $i b^{2}$\nC. $i^{2} b$\nD. $*-\\frac{i}{b}$\nE. $\\frac{i}{b^{2}}$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "For a system in which the number of particles is fixed, the reciprocal of the Kelvin temperature $T$ is given by which of the following derivatives? (Let $P=$ pressure, $V=$ volume, $S=$ entropy, and $U=$ internal energy.)\n\nA. $\\left(\\frac{\\partial P}{\\partial V}\\right)_{S}$\n\nB. $\\left(\\frac{\\partial P}{\\partial S}\\right)_{V}$\n\nC. $\\left(\\frac{\\partial S}{\\partial P}\\right)_{U}$\n\nD. $\\left(\\frac{\\partial V}{\\partial P}\\right)_{U}$\n\nE. $\\left(\\frac{\\partial S}{\\partial U}\\right)_{V}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "A large isolated system of $N$ weakly interacting particles is in thermal equilibrium. Each particle has only 3 possible nondegenerate states of energies $0, \\epsilon$, and $3 \\epsilon$. When the system is at an absolute temperature $T>\\epsilon / k$, where $k$ is Boltzmann's constant, the average energy of each particle is\nA. 0\nB. $\\epsilon$\nC. $\\frac{4}{3} \\epsilon$\nD. $2 \\epsilon$\nE. $3 \\epsilon$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "If a newly discovered particle $X$ moves with a speed equal to the speed of light in vacuum, then which of the following must be true?\n\nA. The rest mass of $X$ is zero.\n\nB. The spin of $X$ equals the spin of a photon.\n\nC. The charge of $X$ is carried on its surface.\n\nD. $X$ does not spin.\n\nE. $X$ cannot be detected.\n\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A car of rest length 5 meters passes through a garage of rest length 4 meters. Due to the relativistic Lorentz contraction, the car is only 3 meters long in the garage's rest frame. There are doors on both ends of the garage, which open automatically when the front of the car reaches them and close automatically when the rear passes them. The opening or closing of each door requires a negligible amount of time.\n\nThe velocity of the car in the garage's rest frame is\n\nA. $0.4 c$\n\nB. $0.6 c$\n\nC. $0.8 c$\n\nD. greater than $c$\n\nE. not determinable from the data given\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "A car of rest length 5 meters passes through a garage of rest length 4 meters. Due to the relativistic Lorentz contraction, the car is only 3 meters long in the garage's rest frame. There are doors on both ends of the garage, which open automatically when the front of the car reaches them and close automatically when the rear passes them. The opening or closing of each door requires a negligible amount of time.\n\nThe length of the garage in the car's rest frame is\n\nA. $2.4 \\mathrm{~m}$\n\nB. $4.0 \\mathrm{~m}$\n\nC. $5.0 \\mathrm{~m}$\n\nD. $8.3 \\mathrm{~m}$\n\nE. not determinable from the data given\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A car of rest length 5 meters passes through a garage of rest length 4 meters. Due to the relativistic Lorentz contraction, the car is only 3 meters long in the garage's rest frame. There are doors on both ends of the garage, which open automatically when the front of the car reaches them and close automatically when the rear passes them. The opening or closing of each door requires a negligible amount of time.\n\nWhich of the following statements is the best response to the question:\n\n\"Was the car ever inside a closed garage?\"\n\nA. No, because the car is longer than the garage in all reference frames.\n\nB. No, because the Lorentz contraction is not a \"real\" effect.\n\nC. Yes, because the car is shorter than the garage in all reference frames.\n\nD. Yes, because the answer to the question in the garage's rest frame must apply in all reference frames.\n\nE. There is no unique answer to the question, as the order of door openings and closings depends on the reference frame.", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "The measured index of refraction of $x$-rays in rock salt is less than one. This is consistent with the theory of relativity because\n\nA. relativity deals with light waves traveling in a vacuum only\n\nB. $\\mathrm{x}$-rays cannot transmit signals\n\nC. $\\mathrm{x}$-ray photons have imaginary mass\n\nD. the theory of relativity predates the development of solid-state physics\n\nE. the phase velocity and group velocity are different\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "It is necessary to coat a glass lens with a nonreflecting layer. If the wavelength of the light in the coating is $\\lambda$, the best choice is a layer of material having an index of refraction between those of glass and air and a thickness of\nA. $\\frac{\\lambda}{4}$\nB. $\\frac{\\lambda}{2}$\nC. $\\frac{\\lambda}{\\sqrt{2}}$\nD. $\\lambda$\nE. $1.5 \\lambda$\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "Unpolarized light is incident on two ideal polarizers in series. The polarizers are oriented so that no light emerges through the second polarizer. A third polarizer is now inserted between the first two and its orientation direction is continuously rotated through $180^{\\circ}$. The maximum fraction of the incident power transmitted through all three polarizers is\nA. zero\nB. $\\frac{1}{8}$\nC. $\\frac{1}{2}$\nD. $\\frac{1}{\\sqrt{2}}$\nE. 1\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "The period of a hypothetical Earth satellite orbiting at sea level would be 80 minutes. In terms of the Earth's radius $\\boldsymbol{R}_{e}$, the radius of a synchronous satellite orbit (period 24 hours) is most nearly\n\nA. $3 R$\n\nB.\n\nC. $18 R$\n\nD. $320 R_{e}$\n\nE. $5800 R_{e}$\n\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A hoop of mass $M$ and radius $R$ is at rest at the top of an inclined plane as shown above. The hoop rolls down the plane without slipping. When the hoop reaches the bottom, its angular momentum around its center of mass is\n\nA. $M R \\sqrt{g h}$\n\nB. $\\frac{1}{2} M R \\sqrt{g h}$\n\nC. $M \\sqrt{2 g h}$\n\nD. $M g h$\n\nE. $\\frac{1}{2} M g h$\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "A particle is constrained to move along the $x$-axis under the influence of the net force $\\mathbf{F}=-k \\mathbf{x}$ with amplitude $A$ and frequency $f$, where $k$ is a positive constant. When $x=A / 2$, the particle's speed is\nA. $2 \\pi f A$\nB. $\\sqrt{3} \\pi f A$\nC. $\\sqrt{2} \\pi f A$\nD. $\\pi f A$\nE. $\\frac{1}{3} \\pi f A$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A system consists of two charged particles of equal mass. Initially the particles are far apart, have zero potential energy, and one particle has nonzero speed. If radiation is neglected, which of the following is true of the total energy of the system?\n\nA. It is zero and remains zero.\n\nB. It is negative and constant.\n\nC. It is positive and constant.\n\nD. It is constant, but the sign cannot be determined unless the initial velocities of both particles are known.\n\nE. It cannot be a constant of the motion because the particles exert force on each other.\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "One of Maxwell's equations is $\\nabla \\cdot \\mathbf{B}=\\mathbf{0}$. Which of the following sketches shows magnetic field lines that clearly violate this equation within the region bounded by the dashed lines?\n\nA.\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": true}
{"input": "Which of the following electric fields could exist in a finite region of space that contains no charges? (In these expressions, $A$ is a constant, and $\\mathbf{i}, \\mathbf{j}$, and $\\mathbf{k}$ are unit vectors pointing in the $x, y$, and $z$ directions, respectively.)\n\nA. $A(2 x y i-x z k)$\n\nB. $A(-x y \\mathbf{j}+x z \\mathbf{k})$\n\nC. $A(x z \\mathbf{i}+x z \\mathbf{j})$\n\nD. $\\operatorname{Axyz}(\\mathbf{i}+\\mathbf{j})$\n\nE. $A x y z 1$\n\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A small circular wire loop of radius $a$ is located at the center of much larger circular wire loop of radius $b$ as shown above. The larger loop carries an alternating current $I=I_{0} \\cos \\omega t$, where $I_{0}$ and $\\omega$ are constants. The magnetic field generated by the current in the large loop induces in the small loop an emf that is approximately equal to which of the following? (Either use mks units and let $\\mu_{0}$ be the permeability of free space, or use Gaussian units and let $\\mu_{0}$ be $4 \\pi / c^{2}$.)\n\nA. $\\left(\\frac{\\pi \\mu_{0} I_{0}}{2}\\right) \\frac{a^{2}}{b} \\omega \\cos \\omega t$\n\nB. $\\left(\\frac{\\pi \\mu_{0} I_{0}}{2}\\right) \\frac{a^{2}}{b} \\omega \\sin \\omega t$\n\nC. $\\left(\\frac{\\pi \\mu_{0} I_{0}}{2}\\right) \\frac{a}{b^{2}} \\omega \\sin \\omega t$\n\nD. $\\left(\\frac{\\pi \\mu_{0} I_{0}}{2}\\right) \\frac{a}{b^{2}} \\cos \\omega t$\n\nE. $\\left(\\frac{\\pi \\mu_{0} I_{0}}{2}\\right) \\frac{a}{b} \\sin \\omega t$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "The emission spectrum of an atomic gas in a magnetic field differs from that of the gas in the absence of a magnetic field. Which of the following is true of the phenomenon?\n\nA. It is called the Stern-Gerlach effect.\n\nB. It is called the Stark effect.\n\nC. It is due primarily to the nuclear magnetic moment of the atoms.\n\nD. The number of emission lines observed for the gas in a magnetic field is always twice the number observed in the absence of a magnetic field.\n\nE. The number of emission lines observed for the gas in a magnetic field is either greater than or equal to the number observed in the absence of a magnetic field.", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "A spectral line is produced by a gas that is sufficiently dense that the mean time between atomic collisions is much shorter than the mean lives of the atomic states responsible for the line. Compared with the same line produced by a low-density gas, the line produced by the higher-density gas will appear\n\nA. the same\n\nB. more highly polarized\n\nC. broader\n\nD. shifted toward the blue end of the spectrum\n\nE. split into a doublet\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "Sodium has eleven electrons and the sequence in which energy levels fill in atoms is $1 s, 2 s, 2 p$, $3 s, 3 p, 4 s, 3 d$, etc. What is the ground state of sodium in the usual notation ${ }^{2 S+1} L_{J}$ ?\nA. ${ }^{1} S_{0}$\nB. ${ }^{2} S_{\\frac{1}{2}}$\nC. ${ }^{1} P_{0}$\nD. ${ }^{2} P_{\\frac{1}{2}}$\nE. ${ }^{3} P_{\\frac{1}{2}}$\n\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "The figure above shows the photon interaction cross sections for lead in the energy range where the Compton, photoelectric, and pair production processes all play a role. What is the correct identification of these cross sections?\n\nA. 1 = photoelectric, 2 = Compton, 3 = pair production\n\nB. $1=$ photoelectric, $2=$ pair production, $3=$ Compton\n\nC. 1 = Compton, $2=$ pair production, $3=$ photoelectric\n\nD. 1 = Compton, $2=$ photoelectric, $3=$ pair production\n\nE. 1 = pair production, $2=$ photoelectric, $3=$ Compton\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "The exponent in Coulomb's inverse square law has been found to differ from two by less than one part in a billion by measuring which of the following?\n\nA. The charge on an oil drop in the Millikan experiment\n\nB. The deflection of an electron beam in an electric field\n\nC. The neutrality of charge of an atom\n\nD. The electric force between two charged objects\n\nE. The electric field inside a charged conducting shell\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "In a gas of $N$ diatomic molecules, two possible models for a classical description of a diatomic molecule are: [FIGURE]. Which of the following statements about this gas is true? \n\nA. Model I has a specific heat $c_{v}=\frac{3}{2} N k$. \n\nB. Model II has a smaller specific heat than Model I. \n\nC. Model I is always correct. \n\nD. Model II is always correct. \n\nE. The choice between Models I and II dependes on the temperature.", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "Consider a system of $N$ noninteracting particles confined in a volume $V$ at a temperature such that the particles obey classical Boltzmann statistics. If the temperature is lowered to the point at which quantum effects become important, the pressure of the gas may differ depending on whether the particles are fermions or bosons. Let $P_{F}$ be the pressure exerted by the particles if they are fermions, $P_{B}$ be the pressure if they are bosons, and $P_{C}$ be the pressure the particles would exert if quantum effects are ignored. Which of the following is true?\n\nA. $P_{F}=P_{B}=P_{C}$\n\nB. $P_{F}>P_{C}>P_{B}$\n\nC. $P_{F}>P_{B}>P_{C}$\n\nD. $P_{F}<P_{B}<P_{C}$\n\nE. $P_{F}<P_{C}<P_{B}$", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A system containing two identical particles is described by a wave function of the form\n\n$\\psi=\\frac{1}{\\sqrt{2}}\\left[\\psi_{\\alpha}\\left(x_{1}\\right) \\psi_{\\beta}\\left(x_{2}\\right)+\\psi_{\\beta}\\left(x_{1}\\right) \\psi_{\\alpha}\\left(x_{2}\\right)\\right]$\n\nwhere $x_{1}$ and $x_{2}$ represent the spatial coordinates of the particles and $\\alpha$ and $\\beta$ represent all the quantum numbers, including spin, of the states that they occupy. The particles might be\n\nA. electrons\n\nB. positrons\n\nC. protons\n\nD. neutrons\n\nE. deuterons\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "The figure above shows one of the possible energy eigenfunctions $\\psi(x)$ for a particle bouncing freely back and forth along the $x$-axis between impenetrable walls located at $x=-a$ and $x=+a$. The potential energy equals zero for $|x|<a$. If the energy of the particle is 2 electron volts when it is in the quantum state associated with this eigenfunction, what is its energy when it is in the quantum state of lowest possible energy?\nA. $0 \\mathrm{eV}$\nB. $\\frac{1}{\\sqrt{2}} \\mathrm{eV}$\nC. $\\frac{1}{2} \\mathrm{eV}$\nD. $1 \\mathrm{eV}$\nE. $2 \\mathrm{eV}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": true}
{"input": "When a narrow beam of monoenergetic electrons impinges on the surface of a single metal crystal at an angle of 30 degrees with the plane of the surface, first-order reflection is observed. If the spacing of the reflecting crystal planes is known from $x$-ray measurements to be 3 angstroms, the speed of the electrons is most nearly\n\nA. $1.4 \\times 10^{-4} \\mathrm{~m} / \\mathrm{s}$\n\nB. $2.4 \\mathrm{~m} / \\mathrm{s}$\n\nC. $5.0 \\times 10^{3} \\mathrm{~m} / \\mathrm{s}$\n\nD. $2.4 \\times 10^{6} \\mathrm{~m} / \\mathrm{s}$\n\nE. $4.5 \\times 10^{9} \\mathrm{~m} / \\mathrm{s}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "Which of the following is NOT compatible with the selection rule that controls electric dipole emission of photons by excited states of atoms?\n\nA. $\\Delta n$ may have any negative integral value.\n\nB. $\\Delta l= \\pm 1$\n\nC. $\\Delta m_{\\ell}=0, \\pm 1$\n\nD. $\\Delta s= \\pm 1$\n\nE. $\\Delta j= \\pm 1$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "An electric sander has a continuous belt that rubs against a wood surface as shown schematically above. The sander is 100 percent efficient and draws a current of 9 amperes from a 120 -volt line. The belt speed is 10 meters per second. If the sander is pushing against the wood with a normal force of 100 newtons, the coefficient of friction is most nearly\nA. 0.02\nB. 0.2\nC. 0.4\nD. 1.1\nE. 10\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": true}
{"input": "In the circuit shown above, $R_{2}=3 R_{1}$ and the battery of emf $\\varepsilon$ has negligible internal resistance. The resistance of the diode when it allows current to pass through it is also negligible. At time $t=0$, the switch $S$ is closed and the currents and voltages are allowed to reach their asymptotic values. Then at time $t_{1}$, the switch is opened. Which of the following curves most nearly represents the potential at point $A$ as a function of time $t$ ?\n\nA.\n\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "In the cycle shown above, $K L$ and $N M$ represent isotherms, while $K N$ and $L M$ represent reversible adiabats. A system is carried through the Carnot cycle $K L M N$, taking in heat $Q_{2}$ from the hot reservoir $T_{2}$ and releasing heat $Q_{1}$ to the cold reservoir $T_{1}$. All of the following statements are true EXCEPT:\n\nA. $Q_{1} / T_{1}=Q_{2} / T_{2}$\n\nB. The entropy of the hot reservoir decreases.\n\nC. The entropy of the system increases.\n\nD. The work $W$ done is equal to the net heat absorbed, $Q_{2}-Q_{1}$.\n\nE. The efficiency of the cycle is independent of the working substance.", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": true}
{"input": "A particle of mass $M$ is in an infinitely deep square well potential $V$ where\n\n$$\n\\begin{array}{ll}\nV=0 & \\text { for }-a \\leqq x \\leqq a, \\text { and } \\\\\nV=\\infty & \\text { for } x<-a, a<x .\n\\end{array}\n$$\n\nA very small perturbing potential $V^{\\prime}$ is superimposed on $V$ such that\n\n$$\n\\begin{array}{ll}\nV^{\\prime}=\\epsilon\\left(\\frac{a}{2}-|x|\\right) & \\text { for } \\frac{-a}{2} \\leqq x \\leqq \\frac{a}{2}, \\text { and } \\\\\nV^{\\prime}=0 & \\text { for } x<\\frac{-a}{2}, \\frac{a}{2}<x .\n\\end{array}\n$$\n\nIf $\\psi_{0}, \\psi_{1}, \\psi_{2}, \\psi_{3}, \\ldots$ are the energy eigenfunctions for a particle in the infinitely deep square well potential, with $\\psi_{0}$ being the ground state, which of the following statements is correct about the eigenfunction $\\psi_{0}^{\\prime}$ of a particle in the perturbed potential $V+V^{\\prime}$ ?\n\nA. $\\psi_{0}^{\\prime}=a_{00} \\psi_{0}, a_{00} \\neq 0$\n\nB. $\\psi_{0}^{\\prime}=\\sum_{n=0}^{\\infty} a_{0 n} \\psi_{n}$ with $a_{0 n}=0$ for all odd values of $n$\n\nC. $\\psi_{0}^{\\prime}=\\sum_{n=0}^{\\infty} a_{0 n} \\psi_{n}$ with $a_{0 n}=0$ for all even values of $n$\n\nD. $\\psi_{0}^{\\prime}=\\sum_{n=0}^{\\infty} a_{0 n} \\psi_{n}$ with $a_{0 n} \\neq 0$ for all values of $n$\n\nE. None of the above\n\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "Two uniform cylindrical disks of identical mass $M$, radius $R$, and moment of inertia $\\frac{1}{2} M R^{2}$, as shown above, collide on a frictionless, horizontal surface. Disk 1 , having an initial counterclockwise angular velocity $\\omega_{0}$ and a center-of-mass velocity $v_{0}=\\frac{1}{2} \\omega_{0} R$ to the right, makes a grazing collision with disk II initially at rest. If after the collision the two disks stick together, the magnitude of the total angular momentum about the point $P$ is\n\nA. zero\n\nB. $\\frac{1}{2} M R^{2} \\omega_{0}$\n\nC. $\\frac{1}{2} M R v_{0}$\n\nD. $M R v_{0}$\n\nE. dependent on the time of the collision\n\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "The long thin cylindrical glass rod shown above has length $\\ell$ and is insulated from its surroundings. The rod has an excess charge $Q$ uniformly distributed along its length. Assume the electric potential to be zero at infinite distances from the rod. If $k$ is the constant in Coulomb's law, the electric potential at a point $P$ along the axis of the rod and a distance $\\ell$ from one end is $\\frac{k Q}{\\ell}$\nmultiplied by\n\nA. $\\frac{4}{9}$\n\nB. $\\frac{1}{2}$\n\nC. $\\frac{2}{3}$\n\nD. $\\ln 2$\n\nE. 1", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": true}
{"input": "The positronium \"atom\" consists of an electron and a positron bound together by their mutual Coulomb attraction and moving about their center of mass, which is located halfway between them. Thus the positronium \"atom\" is somewhat analogous to a hydrogen atom. The ground-state binding energy of hydrogen is 13.6 electron volts. What is the ground-state binding energy of positronium?\n\nA. $\\left(\\frac{1}{2}\\right)^{2} \\times 13.6 \\mathrm{eV}$\n\nB. $\\frac{1}{2} \\times 13.6 \\mathrm{eV}$\n\nC. $13.6 \\mathrm{eV}$\n\nD. $2 \\times 13.6 \\mathrm{eV}$\n\nE. $(2)^{2} \\times 13.6 \\mathrm{eV}$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "The screen of a pinhole camera is at a distance $D$ from the pinhole, which has a diameter $d$. The light has an effective wavelength $\\lambda .(\\lambda<<D)$ For which of the following values of $d$ will the image be sharpest?\nA. $\\sqrt{\\lambda D}$\nB. $\\lambda$\nC. $\\frac{\\lambda}{10}$\nD. $\\frac{\\lambda^{2}}{D}$\nE. $\\frac{D^{2}}{\\lambda}$\n\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "Which of the following best illustrates the acceleration of a pendulum bob at points $a$ through $e$ ?\n\nA.\n\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": true}
{"input": "The coefficient of static friction between a small coin and the surface of a turntable is 0.30 . The turntable rotates at 33.3 revolutions per minute. What is the maximum distance from the center of the turntable at which the coin will not slide?\n\nA. $0.024 \\mathrm{~m}$\n\nB. $0.048 \\mathrm{~m}$\n\nC. $0.121 \\mathrm{~m}$\n\nD. $0.242 \\mathrm{~m}$\n\nE. $0.484 \\mathrm{~m}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "A satellite of mass $m$ orbits a planet of mass $M$ in a circular orbit of radius $R$. The time required for one revolution is\n\nA. independent of $M$\n\nB. proportional to $\\sqrt{m}$\n\nC. linear in $R$\n\nD. proportional to $R^{3 / 2}$\n\nE. proportional to $R^{2}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "In a nonrelativistic, one-dimensional collision, a particle of mass $2 m$ collides with a particle of mass $m$ at rest. If the particles stick together after the collision, what fraction of the initial kinetic energy is lost in the collision?\n\nA. 0\n\nB. $\\frac{1}{4}$\n\nC. $\\frac{1}{3}$\n\nD. $\\frac{1}{2}$\n\nE. $\\frac{2}{3}$\n\nSCRATCHWORK\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "A three-dimensional harmonic oscillator is in thermal equilibrium with a temperature reservoir at temperature $T$. The average total energy of the oscillator is\n\nA. $\\frac{1}{2} k T$\n\nB. $k T$\n\nC. $\\frac{3}{2} k T$\n\nD. $3 k T$\n\nE. $6 k T$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "An ideal monatomic gas expands quasi-statically to twice its volume. If the process is isothermal, the work done by the gas is $W_{i}$. If the process is adiabatic, the work done by the gas is $W_{a}$. Which of the following is true?\n\nA. $W_{i}=W_{a}$\n\nB. $0=W_{i}<W_{a}$\n\nC. $0<W_{i}<W_{a}$\n\nD. $0=W_{a}<W_{i}$\n\nE. $0<W_{a}<W_{i}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "Two long, identical bar magnets are placed under a horizontal piece of paper, as shown in the figure above. The paper is covered with iron filings. When the two north poles are a small distance apart and touching the paper, the iron filings move into a pattern that shows the magnetic field lines. Which of the following best illustrates the pattern that results?\n\nA.\n\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "A positive charge $Q$ is located at a distance $L$ above an infinite grounded conducting plane, as shown in the figure above. What is the total charge induced on the plane?\n\nA. $2 Q$\n\nB. $Q$\n\nC. 0\n\nD. $-Q$\n\nE. $-2 Q$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": true}
{"input": "Five positive charges of magnitude $q$ are arranged symmetrically around the circumference of a circle of radius $r$. What is the magnitude of the electric field at the center of the circle? $\\left(k=1 / 4 \\pi \\epsilon_{0}\\right)$\n\nA. 0\n\nB. $k q / r^{2}$\n\nC. $5 k q / r^{2}$\n\nD. $\\left(k q / r^{2}\\right) \\cos (2 \\pi / 5)$\n\nE. $\\left(5 k q / r^{2}\\right) \\cos (2 \\pi / 5)$\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A 3-microfarad capacitor is connected in series with a 6 -microfarad capacitor. When a 300 -volt potential difference is applied across this combination, the total energy stored in the two capacitors is\n\nA. $0.09 \\mathrm{~J}$\n\nB. $0.18 \\mathrm{~J}$\n\nC. $0.27 \\mathrm{~J}$\n\nD. $0.41 \\mathrm{~J}$\n\nE. $0.81 \\mathrm{~J}$\n\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "An object is located 40 centimeters from the first of two thin converging lenses of focal lengths 20 centimeters and 10 centimeters, respectively, as shown in the figure above. The lenses are separated by 30 centimeters. The final image formed by the two-lens system is located\n\nA. $5.0 \\mathrm{~cm}$ to the right of the second lens\n\nB. $13.3 \\mathrm{~cm}$ to the right of the second lens\n\nC. infinitely far to the right of the second lens\n\nD. $13.3 \\mathrm{~cm}$ to the left of the second lens\n\nE. $100 \\mathrm{~cm}$ to the left of the second lens\n\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "A spherical, concave mirror is shown in the figure above. The focal point $F$ and the location of the object $O$ are indicated. At what point will the image be located?\n\nA. I\n\nB. II\n\nC. III\n\nD. IV\n\nE. $\\mathrm{V}$\n\nSCRATCHWORK\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "Two stars are separated by an angle of $3 \\times 10^{-5}$ radians. What is the diameter of the smallest telescope that can resolve the two stars using visible light ( $\\lambda \\cong 600$ nanometers) ? (Ignore any effects due to Earth's atmosphere.)\n\nA. $1 \\mathrm{~mm}$\n\nB. $2.5 \\mathrm{~cm}$\n\nC. $10 \\mathrm{~cm}$\n\nD. $2.5 \\mathrm{~m}$\n\nE. $10 \\mathrm{~m}$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "An 8-centimeter-diameter by 8 -centimeter-long $\\mathrm{NaI}(\\mathrm{Tl})$ detector detects gamma rays of a specific energy from a point source of radioactivity. When the source is placed just next to the detector at the center of the circular face, 50 percent of all emitted gamma rays at that energy are detected. If the detector is moved to 1 meter away, the fraction of detected gamma rays drops to\n\nA. $10^{-4}$\n\nB. $2 \\times 10^{-4}$\n\nC. $4 \\times 10^{-4}$\n\nD. $8 \\pi \\times 10^{-4}$\n\nE. $16 \\pi \\times 10^{-4}$", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "Five classes of students measure the height of a building. Each class uses a different method and each measures the height many different times. The data for each class are plotted below. Which class made the most precise measurement?\n\nA.\n\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "A student makes 10 one-second measurements of the disintegration of a sample of a long-lived radioactive isotope and obtains the following values.\n\n$$\n3,0,2,1,2,4,0,1,2,5\n$$\n\nHow long should the student count to establish the rate to an uncertainty of 1 percent?\n\nA. $80 \\mathrm{~s}$\n\nB. $160 \\mathrm{~s}$\n\nC. $2,000 \\mathrm{~s}$\n\nD. $5,000 \\mathrm{~s}$\n\nE. $6,400 \\mathrm{~s}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "The ground state electron configuration for phosphorus, which has 15 electrons, is\n\nA. $1 s^{2} 2 s^{2} 2 p^{6} 3 s^{1} 3 p^{4}$\n\nB. $1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{3}$\n\nC. $1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 d^{3}$\n\nD. $1 s^{2} 2 s^{2} 2 p^{6} 3 s^{1} 3 d^{4}$\n\nE. $1 s^{2} 2 s^{2} 2 p^{6} 3 p^{2} 3 d^{3}$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "The energy required to remove both electrons from the helium atom in its ground state is $79.0 \\mathrm{eV}$. How much energy is required to ionize helium (i.e., to remove one electron)?\n\nA. $24.6 \\mathrm{eV}$\n\nB. $39.5 \\mathrm{eV}$\n\nC. $51.8 \\mathrm{eV}$\n\nD. $54.4 \\mathrm{eV}$\n\nE. $65.4 \\mathrm{eV}$", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "The primary source of the Sun's energy is a series of thermonuclear reactions in which the energy produced is $c^{2}$ times the mass difference between\n\nA. two hydrogen atoms and one helium atom\n\nB. four hydrogen atoms and one helium atom\n\nC. six hydrogen atoms and two helium atoms\n\nD. three helium atoms and one carbon atom\n\nE. two hydrogen atoms plus two helium atoms and one carbon atom\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "In the production of $X$ rays, the term \"bremsstrahlung\" refers to which of the following?\n\nA. The cut-off wavelength, $\\lambda_{\\min }$, of the $X$-ray tube\n\nB. The discrete $\\mathrm{X}$-ray lines emitted when an electron in an outer orbit fills a vacancy in an inner orbit of the atoms in the target metal of the X-ray tube\n\nC. The discrete X-ray lines absorbed when an electron in an inner orbit fills a vacancy in an outer orbit of the atoms in the target metal of the X-ray tube\n\nD. The smooth, continuous X-ray spectra produced by high-energy blackbody radiation from the $\\mathrm{X}$-ray tube\n\nE. The smooth, continuous X-ray spectra produced by rapidly decelerating electrons in the target metal of the X-ray tube\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "In the hydrogen spectrum, the ratio of the wavelengths for Lyman- $\\alpha$ radiation ( $n=2$ to $n=1)$ to Balmer- $\\alpha$ radiation $(n=3$ to $n=2)$ is\n\nA. $5 / 48$\n\nB. $5 / 27$\n\nC. $1 / 3$\n\nD. 3\n\nE. $27 / 5$\n\nSCRATCHWORK\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "An astronomer observes a very small moon orbiting a planet and measures the moon's minimum and maximum distances from the planet's center and the moon's maximum orbital speed. Which of the following CANNOT be calculated from these measurements?\n\nA. Mass of the moon\n\nB. Mass of the planet\n\nC. Minimum speed of the moon\n\nD. Period of the orbit\n\nE. Semimajor axis of the orbit", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A particle is constrained to move in a circle with a 10 -meter radius. At one instant, the particle's speed is 10 meters per second and is increasing at a rate of 10 meters per second squared. The angle between the particle's velocity and acceleration vectors is\n\nA. $0^{\\circ}$\n\nB. $30^{\\circ}$\n\nC. $45^{\\circ}$\n\nD. $60^{\\circ}$\n\nE. $90^{\\circ}$\n\nSCRATCHWORK\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "A stone is thrown at an angle of $45^{\\circ}$ above the horizontal $x$-axis in the $+x$-direction. If air resistance is ignored, which of the velocity versus time graphs shown above best represents $v_{x}$ versus $t$ and $v_{y}$ versus $t$, respectively?\n\n\\begin{tabular}{|c|c|c|}\n\\hline & $v_{x}$ vs. $t$ & $v_{y} \\mathrm{vs}$ \n\nA. & I & IV \n\nB. & II & \n\nC. & II & III \n\nD. & II & V \n\nE. & IV & V \\\\\n\\hline\n\\end{tabular}\n\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": true}
{"input": "Seven pennies are arranged in a hexagonal, planar pattern so as to touch each neighbor, as shown in the figure above. Each penny is a uniform disk of mass $m$ and radius $r$. What is the moment of inertia of the system of seven pennies about an axis that passes through the center of the central penny and is normal to the plane of the pennies?\n\nA. $(7 / 2) m r^{2}$\n\nB. $(13 / 2) m r^{2}$\n\nC. $(29 / 2) m r^{2}$\n\nD. $(49 / 2) m r^{2}$\n\nE. $(55 / 2) m r^{2}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "A thin uniform rod of mass $M$ and length $L$ is positioned vertically above an anchored frictionless pivot point, as shown above, and then allowed to fall to the ground. With what speed does the free end of the rod strike the ground?\n\nA. $\\sqrt{\\frac{1}{3} g L}$\n\nB. $\\sqrt{g L}$\n\nC. $\\sqrt{3 g L}$\n\nD. $\\sqrt{12 g L}$\n\nE. $12 \\sqrt{g L}$", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": true}
{"input": "The eigenvalues of a Hermitian operator are always\n\nA. real\n\nB. imaginary\n\nC. degenerate\n\nD. linear\n\nE. positive\n\n$$\n\\begin{gathered}\n\\left|\\psi_{1}\\right\\rangle=5|1\\rangle-3|2\\rangle+2|3\\rangle \\\\\n\\left|\\psi_{2}\\right\\rangle=|1\\rangle-5|2\\rangle+x|3\\rangle\n\\end{gathered}\n$$\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "The states $|1\\rangle,|2\\rangle$, and $|3\\rangle$ are orthonormal. For what value of $x$ are the states $\\left|\\psi_{1}\\right\\rangle$ and $\\left|\\psi_{2}\\right\\rangle$ given above orthogonal?\n\nA. 10\n\nB. 5\n\nC. 0\n\nD. -5\n\nE. -10\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "The state $\\psi=\\frac{1}{\\sqrt{6}} \\psi_{-1}+\\frac{1}{\\sqrt{2}} \\psi_{1}+\\frac{1}{\\sqrt{3}} \\psi_{2}$ is a linear combination of three orthonormal eigenstates of the operator $\\hat{O}$ corresponding to eigenvalues $-1,1$, and 2 . What is the expectation value of $\\hat{O}$ for this state?\n\nA. $\\frac{2}{3}$\n\nB. $\\sqrt{\\frac{7}{6}}$\n\nC. 1\n\nD. $\\frac{4}{3}$\n\nE. $\\frac{(\\sqrt{3}+2 \\sqrt{2}-1)}{\\sqrt{6}}$\n\nSCRATCHWORK\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "Which of the following functions could represent the radial wave function for an electron in an atom? ( $r$ is the distance of the electron from the nucleus; $A$ and $b$ are constants.)\nI. $A \\mathrm{e}^{-b r}$\n\nII. $A \\sin (b r)$\n\nIII. $A / r$\n\nA. I only\n\nB. II only\n\nC. I and II only\n\nD. I and III only\n\nE. I, II, and III\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "Positronium is an atom formed by an electron and a positron (antielectron). It is similar to the hydrogen atom, with the positron replacing the proton. If a positronium atom makes a transition from the state with $n=3$ to a state with $n=1$, the energy of the photon emitted in this transition is closest to\n\nA. $6.0 \\mathrm{eV}$\n\nB. $6.8 \\mathrm{eV}$\n\nC. $12.2 \\mathrm{eV}$\n\nD. $13.6 \\mathrm{eV}$\n\nE. $24.2 \\mathrm{eV}$\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "If the total energy of a particle of mass $m$ is equal to twice its rest energy, then the magnitude of the particle's relativistic momentum is\n\nA. $m c / 2$\n\nB. $m c / \\sqrt{2}$\n\nC. $m c$\n\nD. $\\sqrt{3} m c$\n\nE. $2 m c$", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "If a charged pion that decays in $10^{-8}$ second in its own rest frame is to travel 30 meters in the laboratory before decaying, the pion's speed must be most nearly\n\nA. $0.43 \\times 10^{8} \\mathrm{~m} / \\mathrm{s}$\n\nB. $2.84 \\times 10^{8} \\mathrm{~m} / \\mathrm{s}$\n\nC. $2.90 \\times 10^{8} \\mathrm{~m} / \\mathrm{s}$\n\nD. $2.98 \\times 10^{8} \\mathrm{~m} / \\mathrm{s}$\n\nE. $3.00 \\times 10^{8} \\mathrm{~m} / \\mathrm{s}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "In an inertial reference frame $S$, two events occur on the $x$-axis separated in time by $\\Delta t$ and in space by $\\Delta x$. In another inertial reference frame $S^{\\prime}$, moving in the $x$-direction relative to $S$, the two events could occur at the same time under which, if any, of the following conditions?\n\nA. For any values of $\\Delta x$ and $\\Delta t$\n\nB. Only if $|\\Delta x / \\Delta t|<c$\n\nC. Only if $|\\Delta x / \\Delta t|>c$\n\nD. Only if $|\\Delta x / \\Delta t|=c$\n\nE. Under no condition\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "If the absolute temperature of a blackbody is increased by a factor of 3 , the energy radiated per second per unit area does which of the following?\n\nA. Decreases by a factor of 81 .\n\nB. Decreases by a factor of 9 .\n\nC. Increases by a factor of 9 .\n\nD. Increases by a factor of 27.\n\nE. Increases by a factor of 81 .\n\nSCRATCHWORK\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "Consider the quasi-static adiabatic expansion of an ideal gas from an initial state $i$ to a final state $f$. Which of the following statements is NOT true?\n\nA. No heat flows into or out of the gas.\n\nB. The entropy of state $i$ equals the entropy of state $f$.\n\nC. The change of internal energy of the gas is $-\\int P d V$.\n\nD. The mechanical work done by the gas is $\\int P d V$.\n\nE. The temperature of the gas remains constant.\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "A constant amount of an ideal gas undergoes the cyclic process $A B C A$ in the $P V$ diagram shown above. The path $B C$ is isothermal. The work done by the gas during one complete cycle, beginning and ending at $A$, is most nearly\n\nA. $600 \\mathrm{~kJ}$\n\nB. $300 \\mathrm{~kJ}$\n\nC. 0\n\nD. $-300 \\mathrm{~kJ}$\n\nE. $-600 \\mathrm{~kJ}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": true}
{"input": "An AC circuit consists of the elements shown above, with $R=10,000 \\mathrm{ohms}, L=25$ millihenries, and $C$ an adjustable capacitance. The $\\mathrm{AC}$ voltage generator supplies a signal with an amplitude of 40 volts and angular frequency of 1,000 radians per second. For what value of $C$ is the amplitude of the current maximized?\n\nA. $4 \\mathrm{nF}$\n\nB. $40 \\mathrm{nF}$\n\nC. $4 \\mu \\mathrm{F}$\n\nD. $40 \\mu \\mathrm{F}$\n\nE. $400 \\mu \\mathrm{F}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": true}
{"input": "Which two of the following circuits are high-pass filters? [FIGURE] \n\nA. I and II \n\nB. I and III \n\nC. I and IV \n\nD. II and III \n\nE. II and IV", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": true}
{"input": "In the circuit shown above, the switch $S$ is closed at $t=0$. Which of the following best represents the voltage across the inductor, as seen on an oscilloscope?\n\nA. Voltage\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": true}
{"input": "Maxwell's equations can be written in the form shown below. If magnetic charge exists and if it is conserved, which of these equations will have to be changed?\nI. $\\nabla \\cdot \\mathbf{E}=\\rho / \\epsilon_{\\mathrm{o}}$\n\nII. $\\nabla \\cdot \\mathbf{B}=0$\n\nIII. $\\nabla \\times \\mathbf{E}=-\\frac{\\partial \\mathbf{B}}{\\partial t}$\n\nIV. $\\nabla \\times \\mathbf{B}=\\mu_{\\mathrm{o}} \\mathbf{J}+\\mu_{\\mathrm{o}} \\epsilon_{\\mathrm{o}} \\frac{\\partial \\mathbf{E}}{\\partial t}$\n\nA. I only\n\nB. II only\n\nC. III only\n\nD. I and IV\n\nE. II and III\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "Three wire loops and an observer are positioned as shown in the figure above. From the observer's point of view, a current $I$ flows counterclockwise in the middle loop, which is moving towards the observer with a velocity $v$. Loops $A$ and $B$ are stationary. This same observer would notice that\n\nA. clockwise currents are induced in loops $A$ and $B$\n\nB. counterclockwise currents are induced in loops $A$ and $B$\n\nC. a clockwise current is induced in loop $A$, but a counterclockwise current is induced in loop $B$\n\nD. a counterclockwise current is induced in loop $A$, but a clockwise current is induced in loop $B$\n\nE. a counterclockwise current is induced in loop $A$, but no current is induced in loop $B$\n\nSCRATCHWORK\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": true}
{"input": "The components of the orbital angular momentum operator $\\mathbf{L}=\\left(L_{x}, L_{y}, L_{z}\\right)$ satisfy the following commutation relations.\n\n$\\left[L_{x}, L_{y}\\right]=i \\hbar L_{z}$,\n\n$\\left[L_{y}, L_{z}\\right]=i \\hbar L_{x}$,\n\n$\\left[L_{z}, L_{x}\\right]=i \\hbar L_{y}$.\n\nWhat is the value of the commutator $\\left[L_{x} L_{y}, L_{z}\\right]$ ?\n\nA. $2 i \\hbar L_{x} L_{y}$\n\nB. $i \\hbar\\left(L_{x}^{2}+L_{y}^{2}\\right)$\n\nC. $-i \\hbar\\left(L_{x}^{2}+L_{y}^{2}\\right)$\n\nD. $i \\hbar\\left(L_{x}^{2}-L_{y}^{2}\\right)$\n\nE. $-i \\hbar\\left(L_{x}^{2}-L_{y}^{2}\\right)$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "The energy eigenstates for a particle of mass $m$ in a box of length $L$ have wave functions\n\n$\\phi_{n}(x)=\\sqrt{2 / L} \\sin (n \\pi x / L)$ and energies $E_{n}=n^{2} \\pi^{2} \\hbar^{2} / 2 m L^{2}$, where $n=1,2,3, \\ldots$\n\nAt time $t=0$, the particle is in a state described as follows.\n\n$$\n\\Psi(t=0)=\\frac{1}{\\sqrt{14}}\\left[\\phi_{1}+2 \\phi_{2}+3 \\phi_{3}\\right]\n$$\n\nWhich of the following is a possible result of a measurement of energy for the state $\\Psi$ ?\n\nA. $2 E_{1}$\n\nB. $5 E_{1}$\n\nC. $7 E_{1}$\n\nD. $9 E_{1}$\n\nE. $14 E_{1}$", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "Let $|n\\rangle$ represent the normalized $n^{\\text {th }}$ energy eigenstate of the one-dimensional harmonic oscillator, $H|n\\rangle=\\hbar \\omega\\left(n+\\frac{1}{2}\\right)|n\\rangle$. If $|\\psi\\rangle$ is a normalized ensemble state that can be expanded as a linear combination\n\n$|\\psi\\rangle=\\frac{1}{\\sqrt{14}}|1\\rangle-\\frac{2}{\\sqrt{14}}|2\\rangle+\\frac{3}{\\sqrt{14}}|3\\rangle$ of the eigenstates, what is the expectation value of the energy operator in this ensemble state?\n\nA. $\\frac{102}{14} \\hbar \\omega$\n\nB. $\\frac{43}{14} \\hbar \\omega$\n\nC. $\\frac{23}{14} \\hbar \\omega$\n\nD. $\\frac{17}{\\sqrt{14}} \\hbar \\omega$\n\nE. $\\frac{7}{\\sqrt{14}} \\hbar \\omega$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A free particle with initial kinetic energy $E$ and de Broglie wavelength $\\lambda$ enters a region in which it has potential energy $V$. What is the particle's new de Broglie wavelength?\n\nA. $\\lambda(1+E / V)$\n\nB. $\\lambda(1-V / E)$\n\nC. $\\lambda(1-E / V)^{-1}$\n\nD. $\\lambda(1+V / E)^{1 / 2}$\n\nE. $\\lambda(1-V / E)^{-1 / 2}$\n\nSCRATCHWORK\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "A sealed and thermally insulated container of total volume $V$ is divided into two equal volumes by an impermeable wall. The left half of the container is initially occupied by $n$ moles of an ideal gas at temperature $T$. Which of the following gives the change in entropy of the system when the wall is suddenly removed and the gas expands to fill the entire volume?\n\nA. $2 n R \\ln 2$\n\nB. $n R \\ln 2$\n\nC. $\\frac{1}{2} n R \\ln 2$\n\nD. $-n R \\ln 2$\n\nE. $-2 n R \\ln 2$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A gaseous mixture of $\\mathrm{O}_{2}$ (molecular mass $32 \\mathrm{u}$ ) and $\\mathrm{N}_{2}$ (molecular mass $28 \\mathrm{u}$ ) is maintained at constant temperature. What is the ratio $\\frac{v_{r m s}\\left(\\mathrm{~N}_{2}\\right)}{v_{r m s}\\left(\\mathrm{O}_{2}\\right)}$ of the root-mean-square speeds of the molecules?\n\nA. $\\frac{7}{8}$\n\nB. $\\sqrt{\\frac{7}{8}}$\n\nC. $\\sqrt{\\frac{8}{7}}$\n\nD. $\\left(\\frac{8}{7}\\right)^{2}$\n\nE. $\\ln \\left(\\frac{8}{7}\\right)$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "In a Maxwell-Boltzmann system with two states of energies $\\epsilon$ and $2 \\epsilon$, respectively, and a degeneracy of 2 for each state, the partition function is\n\nA. $\\mathrm{e}^{-\\epsilon / k T}$\n\nB. $2 \\mathrm{e}^{-2 \\epsilon / k T}$\n\nC. $2 \\mathrm{e}^{-3 \\epsilon / k T}$\n\nD. $\\mathrm{e}^{-\\epsilon / k T}+\\mathrm{e}^{-2 \\epsilon / k T}$\n\nE. $2\\left[\\mathrm{e}^{-\\epsilon / k T}+\\mathrm{e}^{-2 \\epsilon / k T}\\right]$", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "At $20^{\\circ} \\mathrm{C}$, a pipe open at both ends resonates at a frequency of 440 hertz. At what frequency does the same pipe resonate on a particularly cold day when the speed of sound is 3 percent lower than it would be at $20^{\\circ} \\mathrm{C}$ ?\n\nA. $414 \\mathrm{~Hz}$\n\nB. $427 \\mathrm{~Hz}$\n\nC. $433 \\mathrm{~Hz}$\n\nD. $440 \\mathrm{~Hz}$\n\nE. $453 \\mathrm{~Hz}$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "Unpolarized light of intensity $I_{0}$ is incident on a series of three polarizing filters. The axis of the second filter is oriented at $45^{\\circ}$ to that of the first filter, while the axis of the third filter is oriented at $90^{\\circ}$ to that of the first filter. What is the intensity of the light transmitted through the third filter?\n\nA. 0\n\nB. $I_{0} / 8$\n\nC. $I_{0} / 4$\n\nD. $I_{0} / 2$\n\nE. $I_{0} / \\sqrt{2}$\n\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "The conventional unit cell of a body-centered cubic Bravais lattice is shown in the figure above. The conventional cell has volume $a^{3}$. What is the volume of the primitive unit cell?\n\nA. $a^{3} / 8$\n\nB. $a^{3} / 4$\n\nC. $a^{3} / 2$\n\nD. $a^{3}$\n\nE. $2 a^{3}$\n\nSCRATCHWORK\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": true}
{"input": "Which of the following best represents the temperature dependence of the resistivity of an undoped semiconductor?\n\nA.\n\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "The figure above shows a plot of the timedependent force $F_{x}(t)$ acting on a particle in motion along the $x$-axis. What is the total impulse delivered to the particle?\n\nA. 0\n\nB. $1 \\mathrm{~kg} \\cdot \\mathrm{m} / \\mathrm{s}$\n\nC. $2 \\mathrm{~kg} \\cdot \\mathrm{m} / \\mathrm{s}$\n\nD. $3 \\mathrm{~kg} \\cdot \\mathrm{m} / \\mathrm{s}$\n\nE. $4 \\mathrm{~kg} \\cdot \\mathrm{m} / \\mathrm{s}$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": true}
{"input": "A particle of mass $m$ is moving along the $x$-axis with speed $v$ when it collides with a particle of mass $2 m$ initially at rest. After the collision, the first particle has come to rest, and the second particle has split into two equal-mass pieces that move at equal angles $\\theta>0$ with the $x$-axis, as shown in the figure above. Which of the following statements correctly describes the speeds of the two pieces?\n\nA. Each piece moves with speed $v$.\n\nB. One of the pieces moves with speed $v$, the other moves with speed less than $v$.\n\nC. Each piece moves with speed $v / 2$.\n\nD. One of the pieces moves with speed $v / 2$, the other moves with speed greater than $v / 2$.\n\nE. Each piece moves with speed greater than $v / 2$.\n\nSCRATCHWORK\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "A balloon is to be filled with helium and used to suspend a mass of 300 kilograms in air. If the mass of the balloon is neglected, which of the following gives the approximate volume of helium required? (The density of air is 1.29 kilograms per cubic meter and the density of helium is 0.18 kilogram per cubic meter.)\n\nA. $50 \\mathrm{~m}^{3}$\n\nB. $95 \\mathrm{~m}^{3}$\n\nC. $135 \\mathrm{~m}^{3}$\n\nD. $270 \\mathrm{~m}^{3}$\n\nE. $540 \\mathrm{~m}^{3}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "A stream of water of density $\\rho$, cross-sectional area $A$, and speed $v$ strikes a wall that is perpendicular to the direction of the stream, as shown in the figure above. The water then flows sideways across the wall. The force exerted by the stream on the wall is\n\nA. $\\rho v^{2} A$\n\nB. $\\rho v A / 2$\n\nC. $\\rho g h A$\n\nD. $v^{2} A / \\rho$\n\nE. $v^{2} A / 2 \\rho$", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "A proton moves in the $+z$-direction after being accelerated from rest through a potential difference $V$. The proton then passes through a region with a uniform electric field $E$ in the $+x$-direction and a uniform magnetic field $B$ in the $+y$-direction, but the proton's trajectory is not affected. If the experiment were repeated using a potential difference of $2 \\mathrm{~V}$, the proton would then be\n\nA. deflected in the $+x$-direction\n\nB. deflected in the $-x$-direction\n\nC. deflected in the $+y$-direction\n\nD. deflected in the $-y$-direction\n\nE. undeflected\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "For an inductor and capacitor connected in series, the equation describing the motion of charge is\n\n$$\nL \\frac{d^{2} Q}{d t^{2}}+\\frac{1}{C} Q=0\n$$\n\nwhere $L$ is the inductance, $C$ is the capacitance, and $Q$ is the charge. An analogous equation can be written for a simple harmonic oscillator with position $x$, mass $m$, and spring constant $k$. Which of the following correctly lists the mechanical analogs of $L, C$, and $Q$ ?\n\n\\begin{tabular}{cccc} \n& $\\underline{L}$ & $\\underline{C}$ & $\\underline{Q}$ \\\\\nA. & $m$ & $k$ & $x$ \\\\\nB. & $m$ & $1 / k$ & $x$ \\\\\nC. & $k$ & $x$ & $m$ \\\\\nD. & $1 / k$ & $1 / m$ & $x$ \\\\\nE. & $x$ & $1 / k$ & $1 / m$\n\\end{tabular}\n\nSCRATCHWORK\n\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "An infinite, uniformly charged sheet with surfacecharge density $\\sigma$ cuts through a spherical Gaussian surface of radius $R$ at a distance $x$ from its center, as shown in the figure above. The electric flux $\\Phi$ through the Gaussian surface is\n\nA. $\\frac{\\pi R^{2} \\sigma}{\\epsilon_{0}}$\n\nB. $\\frac{2 \\pi R^{2} \\sigma}{\\epsilon_{0}}$\n\nC. $\\frac{\\pi(R-x)^{2} \\sigma}{\\epsilon_{0}}$\n\nD. $\\frac{\\pi\\left(R^{2}-x^{2}\\right) \\sigma}{\\epsilon_{0}}$\n\nE. $\\frac{2 \\pi\\left(R^{2}-x^{2}\\right) \\sigma}{\\epsilon_{0}}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": true}
{"input": "An electromagnetic plane wave, propagating in vacuum, has an electric field given by $E=E_{0} \\cos (k x-\\omega t)$ and is normally incident on a perfect conductor at $x=0$, as shown in the figure above. Immediately to the left of the conductor, the total electric field $E$ and the total magnetic field $B$ are given by which of the following?\n$\\underline{E}$\n$\\underline{B}$\nA. 0\n0\nB. $2 E_{0} \\cos \\omega t$\n0\nC. 0 $\\left(2 E_{0} / c\\right) \\cos \\omega t$\nD. $2 E_{0} \\cos \\omega t$ $\\left(2 E_{0} / c\\right) \\cos \\omega t$\nE. $2 E_{0} \\cos \\omega t$\n$\\left(2 E_{0} / c\\right) \\sin \\omega t$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": true}
{"input": "A nonrelativistic particle with a charge twice that of an electron moves through a uniform magnetic field. The field has a strength of $\\pi / 4$ tesla and is perpendicular to the velocity of the particle. What is the particle's mass if it has a cyclotron frequency of 1,600 hertz?\n\nA. $2.5 \\times 10^{-23} \\mathrm{~kg}$\n\nB. $1.2 \\times 10^{-22} \\mathrm{~kg}$\n\nC. $3.3 \\times 10^{-22} \\mathrm{~kg}$\n\nD. $5.0 \\times 10^{-21} \\mathrm{~kg}$\n\nE. $7.5 \\times 10^{-21} \\mathrm{~kg}$\n\nSCRATCHWORK\n\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "The distribution of relative intensity $I(\\lambda)$ of blackbody radiation from a solid object versus the wavelength $\\lambda$ is shown in the figure above. If the Wien displacement law constant is $2.9 \\times 10^{-3} \\mathrm{~m} \\cdot \\mathrm{K}$, what is the approximate temperature of the object?\n\nA. $10 \\mathrm{~K}$\n\nB. $50 \\mathrm{~K}$\n\nC. $250 \\mathrm{~K}$\n\nD. $1,500 \\mathrm{~K}$\n\nE. $6,250 \\mathrm{~K}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": true}
{"input": "Electromagnetic radiation provides a means to probe aspects of the physical universe. Which of the following statements regarding radiation spectra is NOT correct?\n\nA. Lines in the infrared, visible, and ultraviolet regions of the spectrum reveal primarily the nuclear structure of the sample.\n\nB. The wavelengths identified in an absorption spectrum of an element are among those in its emission spectrum.\n\nC. Absorption spectra can be used to determine which elements are present in distant stars.\n\nD. Spectral analysis can be used to identify the composition of galactic dust.\n\nE. Band spectra are due to molecules.\n\n$$\nC=3 k N_{A}\\left(\\frac{h v}{k T}\\right)^{2} \\frac{\\mathrm{e}^{h v / k T}}{\\left(\\mathrm{e}^{h v / k T}-1\\right)^{2}}\n$$\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "Einstein's formula for the molar heat capacity $C$ of solids is given above. At high temperatures, $C$ approaches which of the following?\n\nA. 0\n\nB. $3 k N_{A}\\left(\\frac{h v}{k T}\\right)$\n\nC. $3 k N_{A} h v$\n\nD. $3 k N_{A}$\n\nE. $N_{A} h v$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": true}
{"input": "A sample of radioactive nuclei of a certain element can decay only by $\\gamma$-emission and $\\beta$-emission. If the half-life for $\\gamma$-emission is 24 minutes and that for $\\beta$-emission is 36 minutes, the half-life for the sample is\n\nA. 30 minutes\n\nB. 24 minutes\n\nC. 20.8 minutes\n\nD. 14.4 minutes\n\nE. 6 minutes\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "The ${ }^{238} \\mathrm{U}$ nucleus has a binding energy of about 7.6 $\\mathrm{MeV}$ per nucleon. If the nucleus were to fission into two equal fragments, each would have a kinetic energy of just over $100 \\mathrm{MeV}$. From this, it can be concluded that\n\nA. ${ }^{238} \\mathrm{U}$ cannot fission spontaneously\n\nB. ${ }^{238} \\mathrm{U}$ has a large neutron excess\n\nC. nuclei near $A=120$ have masses greater than half that of ${ }^{238} \\mathrm{U}$\n\nD. nuclei near $A=120$ must be bound by about 6.7 $\\mathrm{MeV} /$ nucleon\n\nE. nuclei near $A=120$ must be bound by about 8.5 MeV/nucleon\n\nSCRATCHWORK\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "When ${ }_{4}^{7} \\mathrm{Be}$ transforms into ${ }_{3}^{7} \\mathrm{Li}$, it does so by\n\nA. emitting an alpha particle only\n\nB. emitting an electron only\n\nC. emitting a neutron only\n\nD. emitting a positron only\n\nE. electron capture by the nucleus with emission of a neutrino\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "Blue light of wavelength 480 nanometers is most strongly reflected off a thin film of oil on a glass slide when viewed near normal incidence. Assuming that the index of refraction of the oil is 1.2 and that of the glass is 1.6 , what is the minimum thickness of the oil film (other than zero)?\n\nA. $150 \\mathrm{~nm}$\n\nB. $200 \\mathrm{~nm}$\n\nC. $300 \\mathrm{~nm}$\n\nD. $400 \\mathrm{~nm}$\n\nE. $480 \\mathrm{~nm}$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "Light from a laser falls on a pair of very narrow slits separated by 0.5 micrometer, and bright fringes separated by 1.0 millimeter are observed on a distant screen. If the frequency of the laser light is doubled, what will be the separation of the bright fringes?\n\nA. $0.25 \\mathrm{~mm}$\n\nB. $0.5 \\mathrm{~mm}$\n\nC. $1.0 \\mathrm{~mm}$\n\nD. $2.0 \\mathrm{~mm}$\n\nE. $2.5 \\mathrm{~mm}$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "The ultraviolet Lyman alpha line of hydrogen with wavelength 121.5 nanometers is emitted by an astronomical object. An observer on Earth measures the wavelength of the light received from the object to be 607.5 nanometers. The observer can conclude that the object is moving with a radial velocity of\n\nA. $2.4 \\times 10^{8} \\mathrm{~m} / \\mathrm{s}$ toward Earth\n\nB. $2.8 \\times 10^{8} \\mathrm{~m} / \\mathrm{s}$ toward Earth\n\nC. $2.4 \\times 10^{8} \\mathrm{~m} / \\mathrm{s}$ away from Earth\n\nD. $2.8 \\times 10^{8} \\mathrm{~m} / \\mathrm{s}$ away from Earth\n\nE. $12 \\times 10^{8} \\mathrm{~m} / \\mathrm{s}$ away from Earth\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "Two identical blocks are connected by a spring. The combination is suspended, at rest, from a string attached to the ceiling, as shown in the figure above. The string breaks suddenly. Immediately after the string breaks, what is the downward acceleration of the upper block?\n\nA. 0\n\nB. $g / 2$\n\nC. $g$\n\nD. $\\sqrt{2} g$\n\nE. $2 g$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "For the system consisting of the two blocks shown in the figure above, the minimum horizontal force $F$ is applied so that block $B$ does not fall under the influence of gravity. The masses of $A$ and $B$ are 16.0 kilograms and 4.00 kilograms, respectively. The horizontal surface is frictionless and the coefficient of friction between the two blocks is 0.50 . The magnitude of $F$ is most nearly\n\nA. $50 \\mathrm{~N}$\n\nB. $100 \\mathrm{~N}$\n\nC. $200 \\mathrm{~N}$\n\nD. $400 \\mathrm{~N}$\n\nE. $1,600 \\mathrm{~N}$\n\nSCRATCHWORK\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": true}
{"input": "The Lagrangian for a mechanical system is\n\n$$\nL=a \\dot{q}^{2}+b q^{4}\n$$\n\nwhere $q$ is a generalized coordinate and $a$ and $b$ are constants. The equation of motion for this system is\n\nA. $\\dot{q}=\\sqrt{\\frac{b}{a}} q^{2}$\n\nB. $\\dot{q}=\\frac{2 b}{a} q^{3}$\n\nC. $\\ddot{q}=-\\frac{2 b}{a} q^{3}$\n\nD. $\\ddot{q}=+\\frac{2 b}{a} q^{3}$\n\nE. $\\ddot{q}=\\frac{b}{a} q^{3}$\n\n$$\n\\left(\\begin{array}{l}\na_{x}^{\\prime} \\\\\na_{y}^{\\prime} \\\\\na_{z}^{\\prime}\n\\end{array}\\right)=\\left[\\begin{array}{ccc}\n1 / 2 & \\sqrt{3} / 2 & 0 \\\\\n-\\sqrt{3} / 2 & 1 / 2 & 0 \\\\\n0 & 0 & 1\n\\end{array}\\right]\\left(\\begin{array}{l}\na_{x} \\\\\na_{y} \\\\\na_{z}\n\\end{array}\\right)\n$$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "The matrix shown above transforms the components of a vector in one coordinate frame $S$ to the components of the same vector in a second coordinate frame $S^{\\prime}$. This matrix represents a rotation of the reference frame $S$ by\n\nA. $30^{\\circ}$ clockwise about the $x$-axis\n\nB. $30^{\\circ}$ counterclockwise about the $z$-axis\n\nC. $45^{\\circ}$ clockwise about the $z$-axis\n\nD. $60^{\\circ}$ clockwise about the $y$-axis\n\nE. $60^{\\circ}$ counterclockwise about the $z$-axis\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "The mean kinetic energy of the conduction electrons in metals is ordinarily much higher than $k T$ because\n\nA. electrons have many more degrees of freedom than atoms do\n\nB. the electrons and the lattice are not in thermal equilibrium\n\nC. the electrons form a degenerate Fermi gas\n\nD. electrons in metals are highly relativistic\n\nE. electrons interact strongly with phonons", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "An ensemble of systems is in thermal equilibrium with a reservoir for which $k T=0.025 \\mathrm{eV}$.\n\nState $A$ has an energy that is $0.1 \\mathrm{eV}$ above that of state $B$. If it is assumed the systems obey Maxwell-Boltzmann statistics and that the degeneracies of the two states are the same, then the ratio of the number of systems in state $A$ to the number in state $B$ is\n\nA. $\\mathrm{e}^{+4}$\n\nB. $\\mathrm{e}^{+0.25}$\n\nC. 1\n\nD. $\\mathrm{e}^{-0.25}$\n\nE. $\\mathrm{e}^{-4}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "The muon decays with a characteristic lifetime of about $10^{-6}$ second into an electron, a muon neutrino, and an electron antineutrino. The muon is forbidden from decaying into an electron and just a single neutrino by the law of conservation of\n\nA. charge\n\nB. mass\n\nC. energy and momentum\n\nD. baryon number\n\nE. lepton number\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "A particle leaving a cyclotron has a total relativistic energy of $10 \\mathrm{GeV}$ and a relativistic momentum of $8 \\mathrm{GeV} / c$. What is the rest mass of this particle?\n\nA. $0.25 \\mathrm{GeV} / c^{2}$\n\nB. $1.20 \\mathrm{GeV} / c^{2}$\n\nC. $2.00 \\mathrm{GeV} / c^{2}$\n\nD. $6.00 \\mathrm{GeV} / c^{2}$\n\nE. $16.0 \\mathrm{GeV} / c^{2}$\n\nSCRATCHWORK\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "A tube of water is traveling at $1 / 2 c$ relative to the lab frame when a beam of light traveling in the same direction as the tube enters it. What is the speed of light in the water relative to the lab frame? (The index of refraction of water is $4 / 3$.)\n\nA. $1 / 2 c$\n\nB. $2 / 3 c$\n\nC. $5 / 6 c$\n\nD. $10 / 11 c$\n\nE. $c$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "Which of the following is the orbital angular momentum eigenfunction $Y_{\\ell}^{m}(\\theta, \\phi)$ in a state for which the operators $\\mathbf{L}^{2}$ and $L_{z}$ have eigenvalues $6 \\hbar^{2}$ and $-\\hbar$, respectively?\n\nA. $Y_{2}^{1}(\\theta, \\phi)$\n\nB. $Y_{2}^{-1}(\\theta, \\phi)$\n\nC. $\\frac{1}{\\sqrt{2}}\\left[Y_{2}^{1}(\\theta, \\phi)+Y_{2}^{-1}(\\theta, \\phi)\\right]$\n\nD. $Y_{3}^{2}(\\theta, \\phi)$\n\nE. $Y_{3}^{-1}(\\theta, \\phi)$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "Let $|\\alpha\\rangle$ represent the state of an electron with spin up and $|\\beta\\rangle$ the state of an electron with spin down. Valid spin eigenfunctions for a triplet state $\\left({ }^{3} S\\right)$ of a two-electron atom include which of the following?\nI. $|\\alpha\\rangle_{1}|\\alpha\\rangle_{2}$\n\nII. $\\frac{1}{\\sqrt{2}}\\left(|\\alpha\\rangle_{1}|\\beta\\rangle_{2}-|\\alpha\\rangle_{2}|\\beta\\rangle_{1}\\right)$\n\nIII. $\\frac{1}{\\sqrt{2}}\\left(|\\alpha\\rangle_{1}|\\beta\\rangle_{2}+|\\alpha\\rangle_{2}|\\beta\\rangle_{1}\\right)$\n\nA. I only\n\nB. II only\n\nC. III only\n\nD. I and III\n\nE. II and III", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "The state of a spin- $\\frac{1}{2}$ particle can be represented using the eigenstates $|\\uparrow\\rangle$ and $|\\downarrow\\rangle$ of the $S_{z}$ operator.\n\n$$\n\\begin{aligned}\n& S_{z}|\\uparrow\\rangle=\\frac{1}{2} \\hbar|\\uparrow\\rangle \\\\\n& S_{z}|\\downarrow\\rangle=-\\frac{1}{2} \\hbar|\\downarrow\\rangle\n\\end{aligned}\n$$\n\nGiven the Pauli matrix $\\sigma_{x}=\\left(\\begin{array}{ll}0 & 1 \\\\ 1 & 0\\end{array}\\right)$, which of the following is an eigenstate of $S_{x}$ with eigenvalue $-\\frac{1}{2} \\hbar$ ?\n\nA. $|\\downarrow\\rangle$\n\nB. $\\frac{1}{\\sqrt{2}}(|\\uparrow\\rangle+|\\downarrow\\rangle)$\n\nC. $\\frac{1}{\\sqrt{2}}(|\\uparrow\\rangle-|\\downarrow\\rangle)$\n\nD. $\\frac{1}{\\sqrt{2}}(|\\uparrow\\rangle+i|\\downarrow\\rangle)$\n\nE. $\\frac{1}{\\sqrt{2}}(|\\uparrow\\rangle-i|\\downarrow\\rangle)$\n\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "An energy-level diagram of the $n=1$ and $n=2$ levels of atomic hydrogen (including the effects of spin-orbit coupling and relativity) is shown in the figure above. Three transitions are labeled $A, B$, and $C$. Which of the transitions will be possible electric-dipole transitions?\n\nA. $B$ only\n\nB. $C$ only\n\nC. $A$ and $C$ only\n\nD. $B$ and $C$ only\n\nE. $A, B$, and $C$\n\nSCRATCHWORK\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": true}
{"input": "One end of a Nichrome wire of length $2 L$ and cross-sectional area $A$ is attached to an end of another Nichrome wire of length $L$ and crosssectional area $2 A$. If the free end of the longer wire is at an electric potential of 8.0 volts, and the free end of the shorter wire is at an electric potential of 1.0 volt, the potential at the junction of the two wires is most nearly equal to\n\nA. $2.4 \\mathrm{~V}$\n\nB. $3.3 \\mathrm{~V}$\n\nC. $4.5 \\mathrm{~V}$\n\nD. $5.7 \\mathrm{~V}$\n\nE. $6.6 \\mathrm{~V}$\n\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A coil of 15 turns, each of radius 1 centimeter, is rotating at a constant angular velocity $\\omega=300$ radians per second in a uniform magnetic field of 0.5 tesla, as shown in the figure above. Assume at time $t=0$ that the normal $\\hat{\\mathbf{n}}$ to the coil plane is along the $y$-direction and that the selfinductance of the coil can be neglected. If the coil resistance is $9 \\mathrm{ohms}$, what will be the magnitude of the induced current in milliamperes?\n\nA. $225 \\pi \\sin \\omega t$\n\nB. $250 \\pi \\sin \\omega t$\n\nC. $0.08 \\pi \\cos \\omega t$\n\nD. $1.7 \\pi \\cos \\omega t$\n\nE. $25 \\pi \\cos \\omega t$\n\nSCRATCHWORK\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "Two spherical, nonconducting, and very thin shells of uniformly distributed positive charge $Q$ and radius $d$ are located a distance $10 d$ from each other. A positive point charge $q$ is placed inside one of the shells at a distance $d / 2$ from the center, on the line connecting the centers of the two shells, as shown in the figure above. What is the net force on the charge $q$ ?\n\nA. $\\frac{q Q}{361 \\pi \\epsilon_{0} d^{2}}$ to the left\n\nB. $\\frac{q Q}{361 \\pi \\epsilon_{0} d^{2}}$ to the right\n\nC. $\\frac{q Q}{441 \\pi \\epsilon_{0} d^{2}}$ to the left\n\nD. $\\frac{q Q}{441 \\pi \\epsilon_{0} d^{2}}$ to the right\n\nE. $\\frac{360 q Q}{361 \\pi \\epsilon_{0} d^{2}}$ to the left\n\nSCRATCHWORK\n\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "A segment of wire is bent into an arc of radius $R$ and subtended angle $\\theta$, as shown in the figure above. Point $P$ is at the center of the circular segment. The wire carries current $I$. What is the magnitude of the magnetic field at $P$ ?\n\nA. 0\n\nB. $\\frac{\\mu_{0} I \\theta}{(2 \\pi)^{2} R}$\n\nC. $\\frac{\\mu_{0} I \\theta}{4 \\pi R}$\n\nD. $\\frac{\\mu_{0} I \\theta}{4 \\pi R^{2}}$\n\nE. $\\frac{\\mu_{0} I}{2 \\theta R^{2}}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": true}
{"input": "A child is standing on the edge of a merry-goround that has the shape of a solid disk, as shown in the figure above. The mass of the child is 40 kilograms. The merry-go-round has a mass of 200 kilograms and a radius of 2.5 meters, and it is rotating with an angular velocity of $\\omega=2.0$ radians per second. The child then walks slowly toward the center of the-merry-goround. What will be the final angular velocity of the merry-go-round when the child reaches the center? (The size of the child can be neglected.)\n\nA. $2.0 \\mathrm{rad} / \\mathrm{s}$\n\nB. $2.2 \\mathrm{rad} / \\mathrm{s}$\n\nC. $2.4 \\mathrm{rad} / \\mathrm{s}$\n\nD. $2.6 \\mathrm{rad} / \\mathrm{s}$\n\nE. $2.8 \\mathrm{rad} / \\mathrm{s}$\n\nSCRATCHWORK\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "Two identical springs with spring constant $k$ are connected to identical masses of mass $M$, as shown in the figures above. The ratio of the period for the springs connected in parallel (Figure 1) to the period for the springs connected in series (Figure 2) is\n\nA. $\\frac{1}{2}$\n\nB. $\\frac{1}{\\sqrt{2}}$\n\nC. 1\n\nD. $\\sqrt{2}$\n\nE. 2\n\nSCRATCHWORK\n\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "The cylinder shown above, with mass $M$ and radius $R$, has a radially dependent density. The cylinder starts from rest and rolls without slipping down an inclined plane of height $H$. At the bottom of the plane its translational speed is $(8 g H / 7)^{1 / 2}$. Which of the following is the rotational inertia of the cylinder?\n\nA. $\\frac{1}{2} M R^{2}$\n\nB. $\\frac{3}{4} M R^{2}$\n\nC. $\\frac{7}{8} M R^{2}$\n\nD. $M R^{2}$\n\nE. $\\frac{7}{4} M R^{2}$\n\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "Two small equal masses $m$ are connected by an ideal massless spring that has equilibrium length $\\ell_{0}$ and force constant $k$, as shown in the figure above. The system is free to move without friction in the plane of the page. If $p_{1}$ and $p_{2}$ represent the magnitudes of the momenta of the two masses, a Hamiltonian for this system is\n\nA. $\\frac{1}{2}\\left\\{\\frac{p_{1}^{2}}{m}+\\frac{p_{2}^{2}}{m}-2 k\\left(\\ell-\\ell_{0}\\right)\\right\\}$\n\nB. $\\frac{1}{2}\\left\\{\\frac{p_{1}^{2}}{m}+\\frac{p_{2}^{2}}{m}+2 k\\left(\\ell-\\ell_{0}\\right)^{2}\\right\\}$\n\nC. $\\frac{1}{2}\\left\\{\\frac{p_{1}^{2}}{m}+\\frac{p_{2}^{2}}{m}-k\\left(\\ell-\\ell_{0}\\right)\\right\\}$\n\nD. $\\frac{1}{2}\\left\\{\\frac{p_{1}^{2}}{m}+\\frac{p_{2}^{2}}{m}-k\\left(\\ell-\\ell_{0}\\right)^{2}\\right\\}$\n\nE. $\\frac{1}{2}\\left\\{\\frac{p_{1}^{2}}{m}+\\frac{p_{2}^{2}}{m}+k\\left(\\ell-\\ell_{0}\\right)^{2}\\right\\}$\n\nSCRATCHWORK\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "The solution to the Schrödinger equation for the ground state of hydrogen is\n\n$$\n\\psi_{0}=\\frac{1}{\\sqrt{\\pi a_{0}^{3}}} e^{-r / a_{0}}\n$$\n\nwhere $a_{0}$ is the Bohr radius and $r$ is the distance from the origin. Which of the following is the most probable value for $r$ ?\n\nA. 0\n\nB. $a_{0} / 2$\n\nC. $a_{0}$\n\nD. $2 a_{0}$\n\nE. $\\infty$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "The raising and lowering operators for the quantum harmonic oscillator satisfy\n\n$a^{\\dagger}|n\\rangle=\\sqrt{n+1}|n+1\\rangle, a|n\\rangle=\\sqrt{n}|n-1\\rangle$\n\nfor energy eigenstates $|n\\rangle$ with energy $E_{n}$.\n\nWhich of the following gives the first-order shift in the $n=2$ energy level due to the perturbation\n\n$$\n\\Delta H=V\\left(a+a^{\\dagger}\\right)^{2}\n$$\n\nwhere $V$ is a constant?\n\nA. 0\n\nB. $V$\n\nC. $\\sqrt{2} V$\n\nD. $2 \\sqrt{2} V$\n\nE. $5 \\mathrm{~V}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "An infinite slab of insulating material with dielectric constant $K$ and permittivity $\\epsilon=K \\epsilon_{0}$ is placed in a uniform electric field of magnitude $E_{0}$. The field is perpendicular to the surface of the material, as shown in the figure above. The magnitude of the electric field inside the material is\n\nA. $\\frac{E_{0}}{K}$\n\nB. $\\frac{E_{0}}{K \\epsilon_{0}}$\n\nC. $E_{0}$\n\nD. $K \\epsilon_{0} E_{0}$\n\nE. $K E_{0}$\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "A uniformly charged sphere of total charge $Q$ expands and contracts between radii $R_{1}$ and $R_{2}$ at a frequency $f$. The total power radiated by the sphere is\n\nA. proportional to $Q$\n\nB. proportional to $f^{2}$\n\nC. proportional to $f^{4}$\n\nD. proportional to $\\left(R_{2} / R_{1}\\right)$\n\nE. zero\n\nSCRATCHWORK\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "A beam of light has a small wavelength spread $\\delta \\lambda$ about a central wavelength $\\lambda$. The beam travels in vacuum until it enters a glass plate at an angle $\\theta$ relative to the normal to the plate, as shown in the figure above. The index of refraction of the glass is given by $n(\\lambda)$. The angular spread $\\delta \\theta^{\\prime}$ of the refracted beam is given by\n\nA. $\\delta \\theta^{\\prime}=\\left|\\frac{1}{n} \\delta \\lambda\\right|$\n\nB. $\\delta \\theta^{\\prime}=\\left|\\frac{d n(\\lambda)}{d \\lambda} \\delta \\lambda\\right|$\n\nC. $\\delta \\theta^{\\prime}=\\left|\\frac{1}{\\lambda} \\frac{d \\lambda}{d n} \\delta \\lambda\\right|$\n\nD. $\\delta \\theta^{\\prime}=\\left|\\frac{\\sin \\theta}{\\sin \\theta^{\\prime}} \\frac{\\delta \\lambda}{\\lambda}\\right|$\n\nE. $\\delta \\theta^{\\prime}=\\left|\\frac{\\tan \\theta^{\\prime}}{n} \\frac{d n(\\lambda)}{d \\lambda} \\delta \\lambda\\right|$", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "Suppose that a system in quantum state $i$ has energy $E_{i}$. In thermal equilibrium, the expression\n\n$$\n\\frac{\\sum_{i} E_{i} e^{-E_{i} / k T}}{\\sum_{i} e^{-E_{i} / k T}}\n$$\n\nrepresents which of the following?\n\nA. The average energy of the system\n\nB. The partition function\n\nC. Unity\n\nD. The probability to find the system with energy $E_{i}$\n\nE. The entropy of the system\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A photon strikes an electron of mass $m$ that is initially at rest, creating an electron-positron pair. The photon is destroyed and the positron and two electrons move off at equal speeds along the initial direction of the photon. The energy of the photon was\n\nA. $m c^{2}$\n\nB. $2 m c^{2}$\n\nC. $3 m c^{2}$\n\nD. $4 m c^{2}$\n\nE. $5 m c^{2}$\n\nSCRATCHWORK\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "A Michelson interferometer is configured as a wavemeter, as shown in the figure above, so that a ratio of fringe counts may be used to compare the wavelengths of two lasers with high precision. When the mirror in the right arm of the interferometer is translated through a distance $d, 100,000$ interference fringes pass across the detector for green light and 85,865 fringes pass across the detector for red $(\\lambda=632.82$ nanometers $)$ light. The wavelength of the green laser light is\n\nA. $500.33 \\mathrm{~nm}$\n\nB. $543.37 \\mathrm{~nm}$\n\nC. $590.19 \\mathrm{~nm}$\n\nD. $736.99 \\mathrm{~nm}$\n\nE. $858.65 \\mathrm{~nm}$\n\nNO TEST MATERIAL ON THIS PAGE\n\nA. Print and sign your full name in this box:\n\nPRINT:\n\n$$\n\\text { (LAST) }\n$$\n\n(FIRST)\n\n(MIDDLE)\n\nSIGN:\n\nCopy this code in box 6 on your answer sheet. Then fill in the corresponding ovals exactly as shown.\n\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "The wave function of a particle is $e^{i(k x-\\omega t)}$, where $x$ is distance, $t$ is time, and $k$ and $\\omega$ are positive real numbers. The $x$-component of the momentum of the particle is\n\nA. 0\n\nB. $\\hbar \\omega$\n\nC. $\\hbar k$\n\nD. $\\frac{\\hbar \\omega}{c}$\n\nE. $\\frac{\\hbar k}{\\omega}$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "The longest wavelength $x$-ray that can undergo Bragg diffraction in a crystal for a given family of planes of spacing $d$ is\n\nA. $\\frac{d}{4}$\n\nB. $\\frac{d}{2}$\n\nC. $d$\n\nD. $2 d$\n\nE. $4 d$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "The ratio of the energies of the $K$ characteristic $\\mathrm{x}$-rays of carbon $(Z=6)$ to those of magnesium $(Z=12)$ is most nearly\n\nA. $\\frac{1}{4}$\n\nB. $\\frac{1}{2}$\n\nC. 1\n\nD. 2\n\nE. 4\n\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "What is $\\frac{F(R)}{F(2 R)}$ ?\n\nA. 32\n\nB. 8\n\nC. 4\n\nD. 2\n\nE. 1\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "Suppose there is a very small shaft in the Earth such that the point mass can be placed at a radius of $R / 2$. What is $\\frac{F(R)}{F\\left(\\frac{R}{2}\\right)}$ ?\n\nA. 8\n\nB. 4\n\nC. 2\n\nD. $\\frac{1}{2}$\n\nE. $\\frac{1}{4}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "Two wedges, each of mass $m$, are placed next to each other on a flat floor. A cube of mass $M$ is balanced on the wedges as shown above. Assume no friction between the cube and the wedges, but a coefficient of static friction $\\mu<1$ between the wedges and the floor. What is the largest $M$ that can be balanced as shown without motion of the wedges?\n\nA. $\\frac{m}{\\sqrt{2}}$\n\nB. $\\frac{\\mu m}{\\sqrt{2}}$\n\nC. $\\frac{\\mu m}{1-\\mu}$\n\nD. $\\frac{2 \\mu m}{1-\\mu}$\n\nE. All $M$ will balance.\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": true}
{"input": "A cylindrical tube of mass $M$ can slide on a horizontal wire. Two identical pendulums, each of mass $m$ and length $\\ell$, hang from the ends of the tube, as shown above. For small oscillations of the pendulums in the plane of the paper, the eigenfrequencies of the normal modes of oscillation of this system\n\nare $0, \\sqrt{\\frac{g(M+2 m)}{\\ell M}}$, and\n\nA. $\\sqrt{\\frac{g}{\\ell}}$\n\nB. $\\sqrt{\\frac{g}{\\ell} \\frac{M+m}{M}}$\n\nC. $\\sqrt{\\frac{g}{\\ell} \\frac{m}{M}}$\n\nD. $\\sqrt{\\frac{g}{\\ell} \\frac{m}{M+m}}$\n\nE. $\\sqrt{\\frac{g}{\\ell} \\frac{m}{M+2 m}}$\n\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "A solid cone hangs from a frictionless pivot at the origin $O$, as shown above. If $\\hat{\\mathbf{i}}, \\hat{\\mathbf{j}}$, and $\\hat{\\mathbf{k}}$ are unit vectors, and $a, b$, and $c$ are positive constants, which of the following forces $F$ applied to the rim of the cone at a point $P$ results in a torque $\\tau$ on the cone with a negative component $\\tau_{z}$ ?\n\nA. $\\mathbf{F}=a \\hat{\\mathbf{k}}, P$ is $(0, b,-c)$\n\nB. $\\mathbf{F}=-a \\hat{\\mathbf{k}}, P$ is $(0,-b,-c)$\n\nC. $\\mathbf{F}=a \\hat{\\mathbf{j}}, P$ is $(-b, 0,-c)$\n\nD. $\\mathbf{F}=a \\hat{\\mathbf{j}}, P$ is $(b, 0,-c)$\n\nE. $\\mathbf{F}=-a \\hat{\\mathbf{k}}, P$ is $(-b, 0,-c)$\n\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": true}
{"input": "A coaxial cable having radii $a, b$, and $c$ carries equal and opposite currents of magnitude $i$ on the inner and outer conductors. What is the magnitude of the magnetic induction at point $P$ outside of the cable at a distance $r$ from the axis?\nA. Zero\nB. $\\frac{\\mu_{0} i r}{2 \\pi a^{2}}$\nC. $\\frac{\\mu_{0} i}{2 \\pi r}$\nD. $\\frac{\\mu_{0} i}{2 \\pi r} \\frac{c^{2}-r^{2}}{c^{2}-b^{2}}$\nE. $\\frac{\\mu_{0} i}{2 \\pi r} \\frac{r^{2}-b^{2}}{c^{2}-b^{2}}$\n\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "Two positive charges of $q$ and $2 q$ coulombs are located on the $x$-axis at $x=0.5 a$ and $1.5 a$, respectively, as shown above. There is an infinite, grounded conducting plane at $x=0$. What is the magnitude of the net force on the charge $q$ ?\n\nA. $\\frac{1}{4 \\pi \\epsilon_{0}} \\frac{q^{2}}{a^{2}}$\n\nB. $\\frac{1}{4 \\pi \\epsilon_{0}} \\frac{3 q^{2}}{2 a^{2}}$\n\nC. $\\frac{1}{4 \\pi \\epsilon_{0}} \\frac{2 q^{2}}{a^{2}}$\n\nD. $\\frac{1}{4 \\pi \\epsilon_{0}} \\frac{3 q^{2}}{a^{2}}$\n\nE. $\\frac{1}{4 \\pi \\epsilon_{0}} \\frac{7 q^{2}}{2 a^{2}}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "The capacitor in the circuit shown above is initially charged. After closing the switch, how much time elapses until one-half of the capacitor's initial stored energy is dissipated?\n\nA. $R C$\n\nB. $\\frac{R C}{2}$\n\nC. $\\frac{R C}{4}$\n\nD. $2 R C \\ln (2)$\n\nE. $\\frac{R C \\ln (2)}{2}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "Two large conducting plates form a wedge of angle $\\alpha$ as shown in the diagram above. The plates are insulated from each other; one has a potential $V_{0}$ and the other is grounded. Assuming that the plates are large enough so that the potential difference between them is independent of the cylindrical coordinates $z$ and $\\rho$, the potential anywhere between the plates as a function of the angle $\\varphi$ is\n\nA. $\\frac{V_{0}}{\\alpha}$\n\nB. $\\frac{V_{0} \\varphi}{\\alpha}$\n\nC. $\\frac{V_{0} \\alpha}{\\varphi}$\n\nD. $\\frac{V_{0} \\varphi^{2}}{\\alpha}$\n\nE. $\\frac{V_{0} \\alpha}{\\varphi^{2}}$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "Listed below are Maxwell's equations of electromagnetism. If magnetic monopoles exist, which of these equations would be INCORRECT?\nI. $\\operatorname{Curl} \\mathbf{H}=\\mathbf{J}+\\frac{\\partial \\mathbf{D}}{\\partial t}$\n\nII. $\\operatorname{Curl} \\mathbf{E}=-\\frac{\\partial \\mathbf{B}}{\\partial t}$\n\nIII. $\\operatorname{div} \\mathbf{D}=\\rho$\n\nIV. $\\operatorname{div} B=0$\n\nA. IV only\n\nB. I and II\n\nC. I and III\n\nD. II and IV\n\nE. III and IV\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "The total energy of a blackbody radiation source is collected for one minute and used to heat water. The temperature of the water increases from $20.0^{\\circ} \\mathrm{C}$ to $20.5^{\\circ} \\mathrm{C}$. If the absolute temperature of the blackbody\n\nie doubled and the experiment repeated, which of the following statements would be most nearly corre t?\n\nA. I the temperature of the water would increase from $20^{\\circ} \\mathrm{C}$ to a final temperature of $21^{\\circ} \\mathrm{C}$.\n\nB. The temperature of the water would increase from $20^{\\circ} \\mathrm{C}$ to a final temperature of $24^{\\circ} \\mathrm{C}$.\n\nC. The temperature of the water would increase from $20^{\\circ} \\mathrm{C}$ to a final temperature of $28^{\\circ} \\mathrm{C}$.\n\nD. The temperature of the water would increase from $20^{\\circ} \\mathrm{C}$ to a final temperature of $36^{\\circ} \\mathrm{C}$.\n\nE. The water would boil within the one-minute time period.\n\n\\section*{Orovono}\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "A classical model of a diatomic molecule is a springy dumbbell, as shown above, where the dumbbell is free to rotate about axes perpendicular to the spring. In the limit of high temperature, what is the specific heat per mole at constant volume?\n\nA. $\\frac{3}{2} R$\n\nB. $\\frac{5}{2} R$\n\nC. $\\frac{7}{2} R$\n\nD. $\\frac{9}{2} R$\n\nE. $\\frac{11}{2} R$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": true}
{"input": "An engine absorbs heat at a temperature of $727^{\\circ} \\mathrm{C}$ and exhausts heat at a temperature of $527^{\\circ} \\mathrm{C}$. If the engine operates at maximum possible efficiency, for 2000 joules of heat input the amount of work the engine performs is most nearly\n\nA. $400 \\mathrm{~J}$\n\nB. $1450 \\mathrm{~J}$\n\nC. $1600 \\mathrm{~J}$\n\nD. $2000 \\mathrm{~J}$\n\nE. $2760 \\mathrm{~J}$\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "The outputs of two electrical oscillators are compared on an oscilloscope screen. The oscilloscope spot is initially at the center of the screen. Oscillator $Y$ is connected to the vertical terminals of the oscilloscope and oscillator $X$ to the horizontal terminals. Which of the following patterns could appear on the oscilloscope screen, if the frequency of oscillator $Y$ is twice that of oscillator $X$ ?\n\nA.\n\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "In transmitting high frequency signals on a coaxial cable, it is important that the cable be terminated at an end with its characteristic impedance in order to avoid\n\nA. leakage of the signal out of the cable\n\nB. overheating of the cable\n\nC. reflection of signals from the terminated end of the cable\n\nD. attenuation of the signal propagating in the cable\n\nE. production of image currents in the outer conductor\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "Which of the following is most nearly the mass of the Earth? (The radius of the Earth is about $6.4 \\times 10^{6}$ meters.)\n\nA. $6 \\times 10^{24} \\mathrm{~kg}$\n\nB. $6 \\times 10^{27} \\mathrm{~kg}$\n\nC. $6 \\times 10^{30} \\mathrm{~kg}$\n\nD. $6 \\times 10^{33} \\mathrm{~kg}$\n\nE. $6 \\times 10^{36} \\mathrm{~kg}$\n\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "In a double-slit interference experiment, $d$ is the distance between the centers of the slits and $w$ is the width of each slit, as shown in the figure above. For incident plane waves, an interference maximum on a distant screen will be \"missing\" when\n\nA. $d=\\sqrt{2} w$\n\nB. $d=\\sqrt{3} w$\n\nC. $2 d=w$\n\nD. $2 d=3 w$\n\nE. $3 d=2 w$", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": true}
{"input": "A soap film with index of refraction greater than air is formed on a circular wire frame that is held in a vertical plane. The film is viewed by reflected light from a white-light source. Bands of color are observed at the lower parts of the soap film, but the area near the top appears black. A correct explanation for this phenomenon would involve which of the following?\n\nI. The top of the soap film absorbs all of the light incident on it; none is transmitted.\n\nII. The thickness of the top part of the soap film has become much less than a wavelength of visible light.\n\nIII. There is a phase change of $180^{\\circ}$ for all wavelengths of light reflected from the front surface of the soap film.\n\nIV. There is no phase change for any wavelength of light reflected from the back surface of the soap film.\n\nA. I only\n\nB. II and III only\n\nC. III and IV only\n\nD. I, II, and III\n\nE. II, III, and IV\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "A simple telescope consists of two convex lenses, the objective and the eyepiece, which have a common focal point $P$, as shown in the figure above. If the focal length of the objective is 1.0 meter and the angular magnification of the telescope is 10 , what is the optical path length between objective and eyepiece?\n\nA. $0.1 \\mathrm{~m}$\n\nB. $0.9 \\mathrm{~m}$\n\nC. $1.0 \\mathrm{~m}$\n\nD. $1.1 \\mathrm{~m}$\n\nE. $10 \\mathrm{~m}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": true}
{"input": "The Fermi temperature of $\\mathrm{Cu}$ is about $80,000 \\mathrm{~K}$. Which of the following is most nearly equal to the average speed of a conduction electron in $\\mathrm{Cu}$ ?\n\nA. $2 \\times 10^{-2} \\mathrm{~m} / \\mathrm{s}$\n\nB. $2 \\mathrm{~m} / \\mathrm{s}$\n\nC. $2 \\times 10^{2} \\mathrm{~m} / \\mathrm{s}$\n\nD. $2 \\times 10^{4} \\mathrm{~m} / \\mathrm{s}$\n\nE. $2 \\times 10^{6} \\mathrm{~m} / \\mathrm{s}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "Solid argon is held together by which of the following bonding mechanisms?\n\nA. Ionic bond only\n\nB. Covalent bond only\n\nC. Partly covalent and partly ionic bond\n\nD. Metallic bond\n\nE. van der Waals bond\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "In experiments located deep underground, the two types of cosmic rays that most commonly reach the experimental apparatus are\n\nA. alpha particles and neutrons\n\nB. protons and electrons\n\nC. iron nuclei and carbon nuclei\n\nD. muons and neutrinos\n\nE. positrons and electrons\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "A radioactive nucleus decays, with the activity shown in the graph above. The half-life of the nucleus is\n\nA. 2 min\n\nB. $7 \\mathrm{~min}$\n\nC. $11 \\mathrm{~min}$\n\nD. $18 \\mathrm{~min}$\n\nE. $23 \\mathrm{~min}$", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "If a freely moving electron is localized in space to within $\\Delta x_{0}$ of $x_{0}$, its wave function can be described by a wave packet $\\psi(x, t)=\\int_{-\\infty}^{\\infty} e^{i(k x-\\omega t)} f(k) d k$, where $f(k)$ is peaked around a central value $k_{0}$. Which of the following is most nearly the width of the peak in $k$ ?\n\nA. $\\Delta k=\\frac{1}{x_{0}}$\n\nB. $\\Delta k=\\frac{1}{\\Delta x_{0}}$\n\nC. $\\Delta k=\\frac{\\Delta x_{0}}{x_{0}{ }^{2}}$\n\nD. $\\Delta k=\\left(\\frac{\\Delta x_{0}}{x_{0}}\\right) k_{0}$\n\nE. $\\Delta k=\\sqrt{k_{0}^{2}+\\left(\\frac{1}{x_{0}}\\right)^{2}}$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A system is known to be in the normalized state described by the wave function\n\n$$\n\\psi(\\theta, \\varphi)=\\frac{1}{\\sqrt{30}}\\left(5 Y_{4}^{3}+Y_{6}^{3}-2 Y_{6}^{0}\\right)\n$$\n\nwhere the $Y_{l}{ }^{m}(\\theta, \\varphi)$ are the spherical harmonics.\n\nThe probability of finding the system in a state with azimuthal orbital quantum number $m=3$ is\n\nA. 0\n\nB. $\\frac{1}{15}$\n\nC. $\\frac{1}{6}$\n\nD. $\\frac{1}{3}$\n\nE. $\\frac{13}{15}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "An attractive, one-dimensional square well has depth $V_{0}$ as shown above. Which of the following best shows a possible wave function for a bound state?\n\nA.\n\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "Given that the binding energy of the hydrogen atom ground state is $E_{0}=13.6 \\mathrm{eV}$, the binding energy of the $n=2$ state of positronium (positron-electron system) is\n\nA. $8 E_{0}$\n\nB. $4 E_{0}$\n\nC. $E_{0}$\n\nD. $\\frac{E_{0}}{4}$\n\nE. $\\frac{E_{0}}{8}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "In a ${ }^{3} S$ state of the helium atom, the possible values of the total electronic angular momentum quantum number are\n\nA. 0 only\n\nB. 1 only\n\nC. 0 and 1 only\n\nD. $0, \\frac{1}{2}$, and 1\n\nE. 0,1 , and 2\n\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "In the circuit shown above, the resistances are given in ohms and the battery is assumed ideal with emf equal to 3.0 volts.\nThe resistor that dissipates the most power is\nA. $R_{1}$\nB. $R_{2}$\nC. $R_{3}$\nD. $R_{4}$\nE. $R_{5}$\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "In the circuit shown above, the resistances are given in ohms and the battery is assumed ideal with emf equal to 3.0 volts.\nThe voltage across resistor $R_{4}$ is\n\nA. $0.4 \\mathrm{~V}$\n\nB. $0.6 \\mathrm{~V}$\n\nC. $1.2 \\mathrm{~V}$\n\nD. $1.5 \\mathrm{~V}$\n\nE. $3.0 \\mathrm{~V}$\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "A conducting cavity is driven as an electromagnetic resonator. If perfect conductivity is assumed, the transverse and normal field components must obey which of the following conditions at the inner cavity walls?\n\nA. $E_{n}=0, B_{n}=0$\n\nB. $E_{n}=0, B_{t}=0$\n\nC. $E_{t}=0, B_{t}=0$\n\nD. $E_{t}=0, B_{n}=0$\n\nE. None of the above\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "Light of wavelength 5200 angstroms is incident normally on a transmission diffraction grating with 2000 lines per centimeter. The first-order diffraction maximum is at an angle, with respect to the incident beam, that is most nearly\n\nA. $3^{\\circ}$\n\nB. $6^{\\circ}$\n\nC. $9^{\\circ}$\n\nD. $12^{\\circ}$\n\nE. $15^{\\circ}$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A plane-polarized electromagnetic wave is incident normally on a flat, perfectly conducting surface. Upon reflection at the surface, which of the following is true?\n\nA. Both the electric vector and magnetic vector are reversed.\n\nB. Neither the electric vector nor the magnetic vector is reversed.\n\nC. The electric vector is reversed; the magnetic vector is not.\n\nD. The magnetic vector is reversed; the electric vector is not.\n\nE. The directions of the electric and magnetic vectors are interchanged.\n\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "A $\\pi^{0}$ meson (rest-mass energy $135 \\mathrm{MeV}$ ) is moving with velocity $0.8 c \\hat{\\mathbf{k}}$ in the laboratory rest frame when it decays into two photons, $\\gamma_{1}$ and $\\gamma_{2}$. In the $\\pi^{0}$ rest frame, $\\gamma_{1}$ is emitted forward and $\\gamma_{2}$ is emitted backward relative to the $\\pi^{0}$ direction of flight. The velocity of $\\gamma_{2}$ in the laboratory rest frame is\n\nA. $-1.0 c \\hat{\\mathbf{k}}$\n\nB. $-0.2 c \\hat{\\mathbf{k}}$\n\nC. $+0.8 c \\hat{\\mathbf{k}}$\n\nD. $+1.0 c \\hat{\\mathbf{k}}$\n\nE. $+1.8 c \\hat{\\mathbf{k}}$\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "Tau leptons are observed to have an average half-life of $\\Delta t_{1}$ in the frame $S_{1}$ in which the leptons are at rest. In an inertial frame $S_{2}$, which is moving at a speed $v_{12}$ relative to $S_{1}$, the leptons are observed to have an average half-life of $\\Delta t_{2}$. In another inertial reference frame $S_{3}$, which is moving at a speed $v_{13}$ relative to $S_{1}$ and $v_{23}$ relative to $S_{2}$, the leptons have an observed half-life of $\\Delta t_{3}$. Which of the following is a correct relationship among two of the half-lives, $\\Delta t_{1}, \\Delta t_{2}$, and $\\Delta t_{3}$ ?\n\nA. $\\Delta t_{2}=\\Delta t_{1} \\sqrt{1-\\left(v_{12}\\right)^{2} / c^{2}}$\n\nB. $\\Delta t_{1}=\\Delta t_{3} \\sqrt{1-\\left(v_{13}\\right)^{2} / c^{2}}$\n\nC. $\\Delta t_{2}=\\Delta t_{3} \\sqrt{1-\\left(v_{23}\\right)^{2} / c^{2}}$\n\nD. $\\Delta t_{3}=\\Delta t_{2} \\sqrt{1-\\left(v_{23}\\right)^{2} / c^{2}}$\n\nE. $\\Delta t_{1}=\\Delta t_{2} \\sqrt{1-\\left(v_{23}\\right)^{2} / c^{2}}$\n\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "If $n$ is an integer ranging from 1 to infinity, $\\omega$ is an angular frequency, and $t$ is time, then the Fourier series for a square wave, as shown above, is given by which of the following?\n\nA. $V(t)=\\frac{4}{\\pi} \\sum_{1}^{\\infty} \\frac{1}{n} \\sin (n \\omega t)$\n\nB. $V(t)=\\frac{4}{\\pi} \\sum_{0}^{\\infty} \\frac{1}{(2 n+1)} \\sin ((2 n+1) \\omega t)$\n\nC. $V(t)=\\frac{4}{\\pi} \\sum_{1}^{\\infty} \\frac{1}{n} \\cos (n \\omega t)$\n\nD. $V(t)=\\frac{4}{\\pi} \\sum_{0}^{\\infty} \\frac{1}{(2 n+1)} \\cos ((2 n+1) \\omega t)$\n\nE. $V(t)=-\\frac{4}{\\pi}+\\frac{4}{\\pi} \\sum_{i}^{\\infty} \\frac{1}{n^{2}} \\cos (n \\omega t)$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "A rigid cylinder rolls at constant speed without slipping on top of a horizontal plane surface. The acceleration of a point on the circumference of the cylinder at the moment when the point touches the plane is\n\nA. directed forward\n\nB. directed backward\n\nC. directed up\n\nD. directed down\n\nE. zero\n\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "A cylinder with moment of inertia $4 \\mathrm{~kg} \\cdot \\mathrm{m}^{2}$ about a fixed axis initially rotates at 80 radians per second about this axis. A constant torque is applied to slow it down to 40 radians per second.\nThe kinetic energy lost by the cylinder is\n\nA. $80 \\mathrm{~J}$\n\nB. $800 \\mathrm{~J}$\n\nC. $4000 \\mathrm{~J}$\n\nD. $9600 \\mathrm{~J}$\n\nE. $19,200 \\mathrm{~J}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "A cylinder with moment of inertia $4 \\mathrm{~kg} \\cdot \\mathrm{m}^{2}$ about a fixed axis initially rotates at 80 radians per second about this axis. A constant torque is applied to slow it down to 40 radians per second.\nIf the cylinder takes 10 seconds to reach 40 radians per second, the magnitude of the applied torque is\n\nA. $80 \\mathrm{~N} \\cdot \\mathrm{m}$\n\nB. $40 \\mathrm{~N} \\cdot \\mathrm{m}$\n\nC. $32 \\mathrm{~N} \\cdot \\mathrm{m}$\n\nD. $16 \\mathrm{~N} \\cdot \\mathrm{m}$\n\nE. $8 \\mathrm{~N} \\cdot \\mathrm{m}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "If $\\frac{\\partial L}{\\partial q_{n}}=0$, where $L$ is the Lagrangian for a conservative system without constraints and $q_{n}$ is a generalized coordinate, then the generalized momentum $p_{n}$ is\n\nA. an ignorable coordinate\n\nB. constant\n\nC. undefined\n\nD. equal to $\\frac{d}{d t}\\left(\\frac{\\partial L}{\\partial q_{n}}\\right)$\n\nE. equal to the Hamiltonian for the system\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A particle of mass $m$ on the Earth's surface is confined to move on the parabolic curve $y=a x^{2}$, where $y$ is up. Which of the following is a Lagrangian for the particle?\n\nA. $L=\\frac{1}{2} m \\dot{y}^{2}\\left(1+\\frac{1}{4 a y}\\right)-m g y$\n\nB. $L=\\frac{1}{2} m \\dot{y}^{2}\\left(1-\\frac{1}{4 a y}\\right)-m g y$\n\nC. $L=\\frac{1}{2} m \\dot{x}^{2}\\left(1+\\frac{1}{4 a x}\\right)-m g x$\n\nD. $L=\\frac{1}{2} m \\dot{x}^{2}\\left(1+4 a^{2} x^{2}\\right)+m g x$\n\nE. $L=\\frac{1}{2} m \\dot{x}^{2}+\\frac{1}{2} m \\dot{y}^{2}+m g y$\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A ball is dropped from a height $h$. As it bounces off the floor, its speed is 80 percent of what it was just before it hit the floor. The ball will then rise to a height of most nearly\n\nA. $0.94 h$\n\nB. $0.80 h$\n\nC. $0.75 h$\n\nD. $0.64 h$\n\nE. $0.50 h$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "Isotherms and coexistence curves are shown in the $p V$ diagram above for a liquid-gas system. The dashed lines are the boundaries of the labeled regions.\nWhich numbered curve is the critical isotherm?\n\nA. 1\n\nB. 2\n\nC. 3\n\nD. 4\n\nE. 5\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "Isotherms and coexistence curves are shown in the $p V$ diagram above for a liquid-gas system. The dashed lines are the boundaries of the labeled regions.\nIn which region are the liquid and the vapor in equilibrium with each other?\n\nA. $A$\n\nB. $B$\n\nC. $C$\n\nD. $D$\n\nE. $E$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "The magnitude of the force $F$ on an object can be determined by measuring both the mass $m$ of an object and the magnitude of its acceleration $a$, where $F=m a$. Assume that these measurements are uncorrelated and normally distributed. If the standard deviations of the measurements of the mass and the acceleration are $\\sigma_{m}$ and $\\sigma_{a}$, respectively, then $\\sigma_{F} / F$ is\n\nA. $\\left(\\frac{\\sigma_{m}}{m}\\right)^{2}+\\left(\\frac{\\sigma_{a}}{a}\\right)^{2}$\n\nB. $\\left(\\frac{\\sigma_{m}}{m}+\\frac{\\sigma_{a}}{a}\\right)^{\\frac{1}{2}}$\n\nC. $\\left[\\left(\\frac{\\sigma_{m}}{m}\\right)^{2}+\\left(\\frac{\\sigma_{a}}{a}\\right)^{2}\\right]^{\\frac{1}{2}}$\n\nD. $\\frac{\\sigma_{m} \\sigma_{a}}{m a}$\n\nE. $\\frac{\\sigma_{m}}{m}+\\frac{\\sigma_{a}}{a}$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "Two horizontal scintillation counters are located near the Earth's surface. One is 3.0 meters directly above the other. Of the following, which is the largest scintillator resolving time that can be used to distinguish downward-going relativistic muons from upwardgoing relativistic muons using the relative time of the scintillator signals?\n\nA. 1 picosecond\n\nB. 1 nanosecond\n\nC. 1 microsecond\n\nD. 1 millisecond\n\nE. 1 second\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "The state of a quantum mechanical system is described by a wave function $\\psi$. Consider two physical observables that have discrete eigenvalues: observable $A$ with eigenvalues $\\{\\alpha\\}$, and observable $B$ with eigenvalues $\\{\\beta\\}$. Under what circumstances can all wave functions be expanded in a set of basis states, each of which is a simultaneous eigenfunction of both $A$ and $B$ ?\n\nA. Only if the values $\\{\\alpha\\}$ and $\\{\\beta\\}$ are nondegenerate\n\nB. Only if $A$ and $B$ commute\n\nC. Only if $A$ commutes with the Hamiltonian of the system\n\nD. Only if $B$ commutes with the Hamiltonian of the system\n\nE. Under all circumstances\n\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A particle of mass $m$ is confined to an infinitely deep square-well potential:\n\n$$\n\begin{aligned}\n& V(x)=\\infty, x \\leq 0, x \\geq a \\\n& V(x)=0,0<x<a .\n\\end{aligned}\n$$\n\nThe normalized eigenfunctions, labeled by the quantum number $n$, are $\\psi_{n}=\\sqrt{\frac{2}{a}} \\sin \frac{n \\pi x}{a}$.\nFor any state $n$, the expectation value of the momentum of the particle is\n\nA. 0\n\nB. $\\frac{\\hbar n \\pi}{a}$\n\nC. $\\frac{2 h n \\pi}{a}$\n\nD. $\\frac{\\hbar n \\pi}{a}(\\cos n \\pi-1)$\n\nE. $\\frac{-i \\hbar n \\pi}{a}(\\cos n \\pi-1)$\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A particle of mass $m$ is confined to an infinitely deep square-well potential:\n\n$$\n\begin{aligned}\n& V(x)=\\infty, x \\leq 0, x \\geq a \\\n& V(x)=0,0<x<a .\n\\end{aligned}\n$$\n\nThe normalized eigenfunctions, labeled by the quantum number $n$, are $\\psi_{n}=\\sqrt{\frac{2}{a}} \\sin \frac{n \\pi x}{a}$.\nThe eigenfunctions satisfy the condition $\\int_{0}^{a} \\psi_{n}{ }^{*}(x) \\psi_{\\ell}(x) d x=\\delta_{n \\ell}, \\delta_{n \\ell}=1$ if $n=\\ell$, otherwise $\\delta_{n \\ell}=0$. This is a statement that the eigenfunctions are\n\nA. solutions to the Schrödinger equation\n\nB. orthonormal\n\nC. bounded\n\nD. linearly dependent\n\nE. symmetric\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A particle of mass $m$ is confined to an infinitely deep square-well potential:\n\n$$\n\begin{aligned}\n& V(x)=\\infty, x \\leq 0, x \\geq a \\\n& V(x)=0,0<x<a .\n\\end{aligned}\n$$\n\nThe normalized eigenfunctions, labeled by the quantum number $n$, are $\\psi_{n}=\\sqrt{\frac{2}{a}} \\sin \frac{n \\pi x}{a}$.\nA measurement of energy $E$ will always satisfy which of the following relationships?\n\nA. $E \\leq \\frac{\\pi^{2} \\hbar^{2}}{8 m a^{2}}$\n\nB. $E \\geq \\frac{\\pi^{2} \\hbar^{2}}{2 m a^{2}}$\n\nC. $E=\\frac{\\pi^{2} \\hbar^{2}}{8 m a^{2}}$\n\nD. $E=\\frac{n^{2} \\pi^{2} \\hbar^{2}}{8 m a^{2}}$\n\nE. $E=\\frac{\\pi^{2} \\hbar^{2}}{2 m a^{2}}$\n\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A rectangular loop of wire with dimensions shown above is coplanar with a long wire carrying current $I$. The distance between the wire and the left side of the loop is $r$. The loop is pulled to the right as indicated.\nWhat are the directions of the induced current in the loop and the magnetic forces on the left and the right sides of the loop as the loop is pulled?\n\n\\begin{tabular}{lll} \nInduced Current & \\begin{tabular}{l} \nForce on \\\\\nLeft Side\n\\end{tabular} & \\begin{tabular}{l} \nForce on \\\\\nRight Side\n\\end{tabular} \\\\\nA. Counterclockwise & To the left & To the right \\\\\nB. Counterclockwise & To the left & To the left \\\\\nC. Counterclockwise & To the right & To the left \\\\\nD. Clockwise & To the right & To the left \\\\\nE. Clockwise & To the left & To the right\n\\end{tabular}\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "A rectangular loop of wire with dimensions shown above is coplanar with a long wire carrying current $I$. The distance between the wire and the left side of the loop is $r$. The loop is pulled to the right as indicated.\nWhat is the magnitude of the net force on the loop when the induced current is $i$ ?\n\nA. $\\frac{\\mu_{0} i I}{2 \\pi} \\ln \\left(\\frac{r+a}{r}\\right)$\n\nB. $\\frac{\\mu_{0} i I}{2 \\pi} \\ln \\left(\\frac{r}{r+a}\\right)$\n\nC. $\\frac{\\mu_{0} i I}{.2 \\pi} \\frac{b}{a}$\n\nD. $\\frac{\\mu_{0} i I}{2 \\pi} \\frac{a b}{r(r+a)}$\n\nE. $\\frac{\\mu_{0} i I}{2 \\pi} \\frac{r(r+a)}{a b}$", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": true}
{"input": "If $v$ is frequency and $h$ is Planck's constant, the ground state energy of a one-dimensional quantum mechanical harmonic oscillator is\n\nA. 0\n\nB. $\\frac{1}{3} h v$\n\nC. $\\frac{1}{2} h v$\n\nD. $h v$\n\nE. $\\frac{3}{2} h v$\n\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "A uniform and constant magnetic field $B$ is directed perpendicularly into the plane of the page everywhere within a rectangular region as shown above. A wire circuit in the shape of a semicircle is uniformly rotated counterclockwise in the plane of the page about an axis $A$. The axis $A$ is perpendicular to the page at the edge of the field and directed through the center of the straight-line portion of the circuit. Which of the following graphs best approximates the emf $\\varepsilon$ induced in the circuit as a function of time $t$ ?\n\nA.\n\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "The ground state configuration of a neutral sodium atom $(Z=11)$ is\n\nA. $1 s^{2} 2 s^{2} 2 p^{5} 3 s^{2}$\n\nB. $1 s^{2} 2 s^{3} 2 p^{6}$\n\nC. $1 s^{2} 2 s^{2} 2 p^{6} 3 s$\n\nD. $1 s^{2} 2 s^{2} 2 p^{6} 3 p$\n\nE. $l s^{2} 2 s^{2} 2 p^{5}$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "The ground state of the helium atom is a spin\n\nA. singlet\n\nB. doublet\n\nC. triplet\n\nD. quartet\n\nE. quintuplet\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "An electron in a metal has an effective mass $m^{*}=0.1 m_{e}$. If this metal is placed in a magnetic field of magnitude 1 tesla, the cyclotron resonance frequency, $\\omega_{c}$, is most nearly\n\nA. $930 \\mathrm{rad} / \\mathrm{s}$\n\nB. $8.5 \\times 10^{6} \\mathrm{rad} / \\mathrm{s}$\n\nC. $2.8 \\times 10^{11} \\mathrm{rad} / \\mathrm{s}$\n\nD. $1.8 \\times 10^{12} \\mathrm{rad} / \\mathrm{s}$\n\nE. $7.7 \\times 10^{20} \\mathrm{rad} / \\mathrm{s}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "A long, straight, and massless rod pivots about one end in a vertical plane. In configuration I, shown above, two small identical masses are attached to the free end; in configuration II, one mass is moved to the center of the rod. What is the ratio of the frequency of small oscillations of configuration II to that of configuration I ?\n\nA. $(6 / 5)^{\\frac{1}{2}}$\n\nB. $(3 / 2)^{\\frac{1}{2}}$\n\nC. $6 / 5$\n\nD. $3 / 2$\n\nE. $5 / 3$\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "A mole of ideal gas initially at temperature $T_{0}$ and volume $V_{0}$ undergoes a reversible isothermal expansion to volume $V_{1}$. If the ratio of specific heats is $c_{p} / c_{v}=\\gamma$ and if $R$ is the gas constant, the work done by the gas is\n\nA. zero\n\nB. $R T_{0}\\left(V_{1} / V_{0}\\right)^{\\gamma}$\n\nC. $R T_{0}\\left(V_{1} / V_{0}-1\\right)$\n\nD. $c_{v} T_{0}\\left[1-\\left(V_{0} / V_{1}\\right)^{\\gamma^{-1}}\\right]$\n\nE. $R T_{0} \\ln \\left(V_{1} / V_{0}\\right)$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "Which of the following is true if the arrangement of an isolated thermodynamic system is of maximal probability?\n\nA. Spontaneous change to a lower probability occurs.\n\nB. The entropy is a minimum.\n\nC. Boltzmann's constant approaches zero.\n\nD. No spontaneous change occurs.\n\nE. The entropy is zero.\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "If an electric field is given in a certain region by $E_{x}=0, E_{y}=0, E_{z}=k z$, where $k$ is a nonzero constant, which of the following is true?\n\nA. There is a time-varying magnetic field.\n\nB. There is charge density in the region.\n\nC. The electric field cannot be constant in time.\n\nD. The electric field is impossible under any circumstances.\n\nE. None of the above\n\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "Two point charges with the same charge $+Q$ are fixed along the $x$-axis and are a distance $2 R$ apart as shown. A small particle with mass $m$ and charge $-q$ is placed at the midpoint between them. What is the angular frequency $\\omega$ of small oscillations of this particle along the $y$-direction?\n\nA. $\\frac{Q q}{2 \\pi \\epsilon_{0} m R^{2}}$\n\nB. $\\frac{Q q}{4 \\pi \\varepsilon_{0} m R^{2}}$\n\nC. $\\frac{Q q}{2 \\pi \\epsilon_{0} m R^{3}}$\n\nD. $\\left(\\frac{Q q}{4 \\pi \\epsilon_{0} m R^{2}}\\right)^{\\frac{1}{2}}$\n\nE. $\\left(\\frac{Q q}{2 \\pi \\epsilon_{0} m R^{3}}\\right)^{\\frac{1}{2}}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "A thin uniform steel chain is 10 meters long with a mass density of 2 kilograms per meter. One end of the chain is attached to a horizontal axle having a radius that is small compared to the length of the chain. If the chain initially hangs vertically, the work required to slowly wind it up on to the axle is closest to\n\nA. $100 \\mathrm{~J}$\n\nB. $200 \\mathrm{~J}$\n\nC. $1,000 \\mathrm{~J}$\n\nD. $2,000 \\mathrm{~J}$\n\nE. $10,000 \\mathrm{~J}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "A steady beam of light is normally incident on a piece of polaroid. As the polaroid is rotated around the beam axis, the transmitted intensity varies as $A+B \\cos 2 \\theta$, where $\\theta$ is the angle of rotation, and $A$ and $B$ are constants with $A>B>0$. Which of the following may be correctly concluded about the incident light?\n\nA. The light is completely unpolarized.\n\nB. The light is completely plane polarized.\n\nC. The light is partly plane polarized and partly unpolarized.\n\nD. The light is partly circularly polarized and partly unpolarized.\n\nE. The light is completely circularly polarized.\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": true}
{"input": "The angular separation of the two components of a double star is 8 microradians, and the light from the double star has a wavelength of 5500 angstroms. The smallest diameter of a telescope mirror that will resolve the double star is most nearly\n\nA. $1 \\mathrm{~mm}$\n\nB. $1 \\mathrm{~cm}$\n\nC. $10 \\mathrm{~cm}$\n\nD. $1 \\mathrm{~m}$\n\nE. $100 \\mathrm{~m}$", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "A fast charged particle passes perpendicularly through a thin glass sheet of index of refraction 1.5. The particle emits light in the glass. The minimum speed of the particle is\n\nA. $\\frac{1}{3} c$\n\nB. $\\frac{4}{9} c$\n\nC. $\\frac{5}{9} c$\n\nD. $\\frac{2}{3} c$\n\nE. $c$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "A monoenergetic beam consists of unstable particles with total energies 100 times their rest energy. If the particles have rest mass $m$, their momentum is most nearly\n\nA. $m c$\n\nB. $10 \\mathrm{mc}$\n\nC. $70 \\mathrm{mc}$\n\nD. $100 m c$\n\nE. $10^{4} \\mathrm{mc}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "A system in thermal equilibrium at temperature $T$ consists of a large number $N_{0}$ of subsystems, each of which can exist only in two states of energy $E_{1}$ and $E_{2}$, where $E_{2}-E_{1}=\\epsilon>0$. In the expressions that follow, $k$ is the Boltzmann constant.\nFor a system at temperature $T$, the average number of subsystems in the state of energy $E_{1}$ is given by\n\nA. $\\frac{N_{0}}{2}$\n\nB. $\\frac{N_{0}}{1+e^{-\\epsilon / k T}}$\n\nC. $N_{0} e^{-\\epsilon / k T}$\n\nD. $\\frac{N_{0}}{1+e^{\\epsilon / k T}}$\n\nE. $\\frac{N_{0} e^{\\epsilon / k T}}{2}$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A system in thermal equilibrium at temperature $T$ consists of a large number $N_{0}$ of subsystems, each of which can exist only in two states of energy $E_{1}$ and $E_{2}$, where $E_{2}-E_{1}=\\epsilon>0$. In the expressions that follow, $k$ is the Boltzmann constant.\nThe internal energy of this system at any temperature $T$ is given by $E_{1} N_{0}+\\frac{N_{0} \\epsilon}{1+e^{\\epsilon / k T}}$. The heat capacity of the system is given by which of the following expressions?\n\nA. $N_{0} k\\left(\\frac{\\epsilon}{k T}\\right)^{2} \\frac{e^{\\epsilon / k T}}{\\left(1+e^{\\epsilon / k T}\\right)^{2}}$\n\nB. $N_{0} k\\left(\\frac{\\epsilon}{k T}\\right)^{2} \\frac{1}{\\left(1+e^{\\epsilon / k T}\\right)^{2}}$\n\nC. $N_{0} k\\left(\\frac{\\epsilon}{k T}\\right)^{2} e^{-\\epsilon / k T}$\n\nD. $\\frac{N_{0} k}{2}\\left(\\frac{\\epsilon}{k T}\\right)^{2}$\n\nE. $\\frac{3}{2} N_{0} k$\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A system in thermal equilibrium at temperature $T$ consists of a large number $N_{0}$ of subsystems, each of which can exist only in two states of energy $E_{1}$ and $E_{2}$, where $E_{2}-E_{1}=\\epsilon>0$. In the expressions that follow, $k$ is the Boltzmann constant.\nWhich of the following is true of the entropy of the system?\n\nA. It increases without limit with $T$ from zero at $T=0$.\n\nB. It decreases with increasing $T$.\n\nC. It increases from zero at $T=0$ to $N_{0} k \\ln 2$ at arbitrarily high temperatures.\n\nD. It is given by $N_{0} k\\left[\\frac{5}{2} \\ln T-\\ln p+\\right.$ constant $]$.\n\nE. It cannot be calculated from the information given.", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "Two circular hoops, $X$ and $Y$, are hanging on nails in a wall. The mass of $X$ is four times that of $Y$, and the diameter of $X$ is also four times that of $Y$. If the period of small oscillations of $X$ is $T$, the period of small oscillations of $Y$ is\nA. $T$\nB. $T / 2$\nC. $T / 4$\nD. $T / 8$\nE. $T / 16$\n\n$$\n{ }_{92}^{235} \\mathrm{U} \\rightarrow{ }_{90}^{231} \\mathrm{Th}+{ }_{2}^{4} \\mathrm{He}\n$$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A uranium nucleus decays at rest into a thorium nucleus and a helium nucleus, as shown above. Which of the following is true?\n\nA. Each decay product has the same kinetic energy.\n\nB. Each decay product has the same speed.\n\nC. The decay products tend to go in the same direction.\n\nD. The thorium nucleus has more momentum than the helium nucleus.\n\nE. The helium nucleus has more kinetic energy than the thorium nucleus.\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "The configuration of three electrons $1 \\mathrm{~s} 2 \\mathrm{p} 3 \\mathrm{p}$ has which of the following as the value of its maximum possible total angular momentum quantum number?\n\nA. $\\frac{7}{2}$\n\nB. 3\n\nC. $\\frac{5}{2}$\n\nD. 2\n\nE. $\\frac{3}{2}$\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "Consider a heavy nucleus with spin $\\frac{1}{2}$. The magnitude of the ratio of the intrinsic magnetic moment of this nucleus to that of an electron is\n\nA. zero, because the nucleus has no intrinsic magnetic moment\n\nB. greater than 1, because the nucleus contains many protons\n\nC. greater than 1, because the nucleus is so much larger in diameter than the electron\n\nD. less than 1, because of the strong interactions among the nucleons in a nucleus\n\nE. less than 1, because the nucleus has a mass much larger than that of the electron\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "One ice skater of mass $m$ moves with speed $2 v$ to the right, while another of the same mass $m$ moves with speed $v$ toward the left, as shown in Figure I. Their paths are separated by a distance $b$. At $t=0$, when they are both at $x=0$, they grasp a pole of length $b$ and negligible mass. For $t>0$, consider the system as a rigid body of two masses $m$ separated by distance $b$, as shown in Figure II. Which of the following is the correct formula for the motion after $t=0$ of the skater initially at $y=b / 2$ ?\n\nA. $x=2 v t, y=b / 2$\n\nB. $x=v t+0.5 b \\sin (3 v t / b), \\quad y=0.5 b \\cos (3 v t / b)$\n\nC. $x=0.5 v t+0.5 b \\sin (3 v t / b), \\quad y=0.5 b \\cos (3 v t / b)$\n\nD. $x=v t+0.5 b \\sin (6 v t / b), \\quad y=0.5 b \\cos (6 v t / b)$\n\nE. $x=0.5 v t+0.5 b \\sin (6 v t / b), \\quad y=0.5 b \\cos (6 v t / b)$\n\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": true}
{"input": "The dispersion curve shown above relates the angular frequency $\\omega$ to the wave number $k$. For waves with wave numbers lying in the range $k_{1}<k<k_{2}$, which of the following is true of the phase velocity and the group velocity?\n\nA. They are in opposite directions.\n\nB. They are in the same direction and the phase velocity is larger.\n\nC. They are in the same direction and the group velocity is larger.\n\nD. The phase velocity is infinite and the group velocity is finite.\n\nE. They are the same in direction and magnitude.", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "A beam of electrons is accelerated through a potential difference of 25 kilovolts in an x-ray tube. The continuous $x$-ray spectrum emitted by the target of the tube will have a short wavelength limit of most nearly\n\nA. $0.1 \\AA$\n\nB. $0.5 \\AA$\n\nC. $2 \\AA$\n\nD. $25 \\AA$\n\nE. $50 \\AA$\n\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "In the $R L C$ circuit shown above, the applied voltage is\n\n$$\n\\varepsilon(t)=\\varepsilon_{\\mathrm{m}} \\cos \\omega t .\n$$\n\nFor a constant $\\varepsilon_{\\mathrm{m}}$, at what angular frequency $\\omega$ does the current have its maximum steady-state amplitude after the transients have died out?\n\nA. $\\frac{1}{R C}$\n\nB. $\\frac{2 L}{R}$\n\nC. $\\frac{1}{\\sqrt{L C}}$\n\nD. $\\sqrt{\\frac{1}{L C}-\\left(\\frac{R}{2 L}\\right)^{2}}$\n\nE. $\\sqrt{\\left(\\frac{1}{R C}\\right)^{2}-\\left(\\frac{L}{R}\\right)^{2}}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": true}
{"input": "A thin plate of mass $M$, length $L$, and width $2 d$ is mounted vertically on a frictionless axle along the $z$-axis, as shown above. Initially the object is at rest. It is then tapped with a hammer to provide a torque $\\tau$, which produces an angular impulse $\\mathbf{H}$ about the $z$-axis of magnitude $H=\\int \\tau d t$. What is the angular speed $\\omega$ of the plate about the $z$-axis after the tap?\n\nA. $\\frac{H}{2 M d^{2}}$\n\nB. $\\frac{H}{M d^{2}}$\n\nC. $\\frac{2 H}{M d^{2}}$\n\nD. $\\frac{3 H}{M d^{2}}$\n\nE. $\\frac{4 H}{M d^{2}}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": true}
{"input": "Two pith balls of equal mass $M$ and equal charge $q$ are suspended from the same point on long massless threads of length $L$ as shown in the figure above. If $k$ is the Coulomb's law constant, then for small values of $\\theta$, the distance $d$ between the charged pith balls at equilibrium is\n\nA. $\\left(\\frac{2 k q^{2} L}{M g}\\right)^{\\frac{1}{3}}$\n\nB. $\\left(\\frac{k q^{2} L}{M g}\\right)^{\\frac{1}{3}}$\n\nC. $\\left(\\frac{2 k q^{2} L}{M g}\\right)^{\\frac{1}{2}}$\n\nD. $\\left(\\frac{k q^{2} L}{M g}\\right)^{\\frac{1}{2}}$\n\nE. $\\frac{L}{4}$\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "An electron oscillates back and forth along the + and $-x$-axes, consequently emitting electromagnetic radiation. Which of the following statements concerning the radiation is NOT true?\n\nA. The total rate of radiation of energy into all directions is proportional to the square of the electron's acceleration.\n\nB. The total rate of radiation of energy into all directions is proportional to the square of the electron's charge.\n\nC. Far from the electron, the rate at which radiated energy crosses a perpendicular unit area decreases as the inverse square of the distance from the electron.\n\nD. Far from the electron, the rate at which radiated energy crosses a perpendicular unit area is a maximum when the unit area is located on the + or $-x$-axes.\n\nE. Far from the electron, the radiated energy is carried equally by the transverse electric and the transverse magnetic fields.", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "A free electron (rest mass $m_{e}=0.5 \\mathrm{MeV} / \\mathrm{c}^{2}$ ) has a total energy of $1.5 \\mathrm{MeV}$. Its momentum $p$ in units of $\\mathrm{MeV} / \\mathrm{c}$ is about\n\nA. 0.86\n\nB. 1.0\n\nC. 1.4\n\nD. 1.5\n\nE. 2.0\n\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "The circuit shown above is used to measure the size of the capacitance $C$. The $y$-coordinate of the spot on the oscilloscope screen is proportional to the potential difference across $R$, and the $x$-coordinate of the spot is swept at a constant speed $s$. The switch is closed and then opened. One can then calculate $C$ from the shape and the size of the curve on the screen plus a knowledge of which of the following?\n\nA. $V_{0}$ and $R$\n\nB. $s$ and $R$\n\nC. $s$ and $V_{0}$\n\nD. $R$ and $R^{\\prime}$\n\nE. The sensitivity of the oscilloscope\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "A particle of mass $M$ moves in a circular orbit of radius $r$ around a fixed point under the influence of an attractive force $F=\\frac{K}{r^{3}}$, where $K$ is a constant. If the potential energy of the particle is zero at an infinite distance from the force center, the total energy of the particle in the circular orbit is\n\nA. $-\\frac{K}{r^{2}}$\n\nB. $-\\frac{K}{2 r^{2}}$\n\nC. 0\n\nD. $\\frac{K}{2 r^{2}}$\n\nE. $\\frac{K}{r^{2}}$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "A parallel-plate capacitor is connected to a battery. $V_{0}$ is the potential difference between the plates, $Q_{0}$ the charge on the positive plate, $E_{0}$ the magnitude of the electric field, and $D_{0}$ the magnitude of the displacement vector. The original vacuum between the plates is filled with a dielectric and then the battery is disconnected. If the corresponding electrical parameters for the final state of the capacitor are denoted by a subscript $f$, which of the following is true?\n\nA. $V_{f}>V_{0}$\n\nB. $V_{f}<V_{0}$\n\nC. $Q_{f}=Q_{0}$\n\nD. $E_{f}>E_{0}$\n\nE. $D_{f}>D_{0}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "The energy levels for the one-dimensional harmonic oscillator are $h v\\left(n+\\frac{1}{2}\\right), n=0,1,2 \\ldots$ How will the energy levels for the potential shown in the graph above differ from those for the harmonic oscillator?\n\nA. The term $\\frac{1}{2}$ will be changed to $\\frac{3}{2}$.\n\nB. The energy of each level will be doubled.\n\nC. The energy of each level will be halved.\n\nD. Only those for even values of $n$ will be present.\n\nE. Only those for odd values of $n$ will be present.\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "The spacing of the rotational energy levels for the hydrogen molecule $\\mathbf{H}_{2}$ is most nearly\n\nA. $10^{-9} \\mathrm{eV}$\n\nB. $10^{-3} \\mathrm{eV}$\n\nC. $10 \\mathrm{eV}$\n\nD. $10 \\mathrm{MeV}$\n\nE. $100 \\mathrm{MeV}$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "The particle decay $\\Lambda \\rightarrow p+\\pi^{-}$must be a weak interaction because\n\nA. the $\\pi^{-}$is a lepton\n\nB. the $\\Lambda$ has spin zero\n\nC. no neutrino is produced in the decay\n\nD. it does not conserve angular momentum\n\nE. it does not conserve strangeness\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "A flat coil of wire is rotated at a frequency of 10 hertz in the magnetic field produced by three pairs of magnets as shown above. The axis of rotation of the coil lies in the plane of the coil and is perpendicular to the field lines. What is the frequency of the alternating voltage in the coil?\n\nA. $\\frac{10}{6} \\mathrm{~Hz}$\n\nB. $\\frac{10}{3} \\mathrm{~Hz}$\n\nC. $10 \\mathrm{~Hz}$\n\nD. $30 \\mathrm{~Hz}$\n\nE. $60 \\mathrm{~Hz}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": true}
{"input": "The figure above shows a small mass connected to a string, which is attached to a vertical post. If the mass is released when the string is horizontal as shown, the magnitude of the total acceleration of the mass as a function of the angle $\\theta$ is\n\nA. $g \\sin \\theta$\n\nB. $2 g \\cos \\theta$\n\nC. $2 g \\sin \\theta$\n\nD. $g \\sqrt{3 \\cos ^{2} \\theta+1}$\n\nE. $g \\sqrt{3 \\sin ^{2} \\theta+1}$", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "Which of the following is a Lorentz transformation? (Assume a system of units such that the velocity of light is 1 .)\n\nA. $x^{\\prime}=4 x$\n\n$y^{\\prime}=y$\n\n$z^{\\prime}=z$\n\n$t^{\\prime}=.25 t$\n\nB. $x^{\\prime}=x-.75 t$\n\n$y^{\\prime}=y$\n\n$z^{\\prime}=z$\n\n$t^{\\prime}=t$\n\nC. $x^{\\prime}=1.25 x-.75 t$\n\n$y^{\\prime}=y$\n\n$z^{\\prime}=z$\n\n$t^{\\prime}=1.25 t-.75 x$\n\nD. $x^{\\prime}=1.25 x-.75 t$\n\n$y^{\\prime}=y$\n\n$z^{\\prime}=z$\n\n$t^{\\prime}=.75 t-1.25 x$\n\nE. None of the above\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "A beam of $10^{12}$ protons per second is incident on a target containing $10^{20}$ nuclei per square centimeter. At an angle of 10 degrees, there are $10^{2}$ protons per second elastically scattered into a detector that subtends a solid angle of $10^{-4}$ steradians. What is the differential elastic scattering cross section, in units of square centimeters per steradian?\n\nA. $10^{-24}$\n\nB. $10^{-25}$\n\nC. $10^{-26}$\n\nD. $10^{-27}$\n\nE. $10^{-28}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "A gas-filled cell of length 5 centimeters is inserted in one arm of a Michelson interferometer, as shown in the figure above. The interferometer is illuminated by light of wavelength 500 nanometers. As the gas is evacuated from the cell, $\\mathbf{4 0}$ fringes cross a point in the field of view. The refractive index of this gas is most nearly\n\nA. 1.02\n\nB. 1.002\n\nC. 1.0002\n\nD. 1.00002\n\nE. 0.98", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": true}
{"input": "Lattice forces affect the motion of electrons in a metallic crystal, so that the relationship between the energy $E$ and wave number $k$ is not the classical equation $E=\\hbar^{2} k^{2} / 2 m$, where $m$ is the electron mass. Instead, it is possible to use an effective mass $m^{*}$ given by which of the following?\n\nA. $m^{*}=\\frac{1}{2} \\hbar^{2} k\\left(\\frac{d k}{d E}\\right)$\n\nB. $m^{*}=\\frac{\\hbar^{2} k}{\\left(\\frac{d k}{d E}\\right)}$\n\nC. $m^{*}=\\hbar^{2} k\\left(\\frac{d^{2} k}{d E^{2}}\\right)^{\\frac{1}{3}}$\n\nD. $m^{*}=\\frac{\\hbar^{2}}{\\left(\\frac{d^{2} E}{d k^{2}}\\right)}$\n\nE. $m^{*}=\\frac{1}{2} \\hbar^{2} m^{2}\\left(\\frac{d^{2} E}{d k^{2}}\\right)$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "The matrix $A=\\left[\\begin{array}{lll}0 & 1 & 0 \\\\ 0 & 0 & 1 \\\\ 1 & 0 & 0\\end{array}\\right]$\n\nhas three eigenvalues $\\lambda_{i}$ defined by $A v_{i}=\\lambda_{i} v_{i}$. Which of the following statements is NOT true?\n\nA. $\\lambda_{1}+\\lambda_{2}+\\lambda_{3}=0$\n\nB. $\\lambda_{1}, \\lambda_{2}$, and $\\lambda_{3}$ are all real numbers.\n\nC. $\\lambda_{2} \\lambda_{3}=+1$ for some pair of roots.\n\nD. $\\lambda_{1} \\lambda_{2}+\\lambda_{2} \\lambda_{3}+\\lambda_{3} \\lambda_{1}=0$\n\nE. $\\lambda_{i}{ }^{3}=+1, i=1,2,3$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "In perturbation theory, what is the first order correction to the energy of a hydrogen atom (Bohr radius $a_{0}$ ) in its ground state due to the presence of a static electric field $E$ ?\n\nA. Zero\n\nB. $e E a_{0}$\n\nC. $3 e E a_{0}$\n\nD. $\\frac{8 e^{2} E a_{0}^{3}}{3}$\n\nE. $\\frac{8 e^{2} E^{2} a_{0}^{3}}{3}$\n\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A uniform rod of length 10 meters and mass 20 kilograms is balanced on a fulcrum with a 40 -kilogram mass on one end of the rod and a 20-kilogram mass on the other end, as shown above. How far is the fulcrum located from the center of the rod?\n\nA. $0 \\mathrm{~m}$\n\nB. $1 \\mathrm{~m}$\n\nC. $1.25 \\mathrm{~m}$\n\nD. $1.5 \\mathrm{~m}$\n\nE. $2 \\mathrm{~m}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": true}
{"input": "A ball is thrown out of the passenger window of a car moving to the right (ignore air resistance). If the ball is thrown out perpendicular to the velocity of the car, which of the following best depicts the path the ball takes, as viewed from above?\n\nA.\n\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "An object is thrown horizontally from the open window of a building. If the initial speed of the object is $20 \\mathrm{~m} / \\mathrm{s}$ and it hits the ground $2.0 \\mathrm{~s}$ later, from what height was it thrown? (Neglect air resistance and assume the ground is level.)\n\nA. $4.9 \\mathrm{~m}$\n\nB. $9.8 \\mathrm{~m}$\n\nC. $10.0 \\mathrm{~m}$\n\nD. $19.6 \\mathrm{~m}$\n\nE. $39.2 \\mathrm{~m}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "A resistor in a circuit dissipates energy at a rate of $1 \\mathrm{~W}$. If the voltage across the resistor is doubled, what will be the new rate of energy dissipation?\n\nA. $0.25 \\mathrm{~W}$\n\nB. $0.5 \\mathrm{~W}$\n\nC. $1 \\mathrm{~W}$\n\nD. $2 \\mathrm{~W}$\n\nE. $4 \\mathrm{~W}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "An infinitely long, straight wire carrying current $I_{1}$ passes through the center of a circular loop of wire carrying current $I_{2}$, as shown above. The long wire is perpendicular to the plane of the loop. Which of the following describes the magnetic force on the loop?\n\nA. Outward, along a radius of the loop.\n\nB. Inward, along a radius of the loop.\n\nC. Upward, along the axis of the loop.\n\nD. Downward, along the axis of the loop.\n\nE. There is no magnetic force on the loop.\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "De Broglie hypothesized that the linear momentum and wavelength of a free massive particle are related by which of the following constants?\n\nA. Planck's constant\n\nB. Boltzmann's constant\n\nC. The Rydberg constant\n\nD. The speed of light\n\nE. Avogadro's number\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "An atom has filled $n=1$ and $n=2$ levels. How many electrons does the atom have?\n\nA. 2\n\nB. 4\n\nC. 6\n\nD. 8\n\nE. 10", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "The root-mean-square speed of molecules of mass $m$ in an ideal gas at temperature $T$ is\n\nA. 0\n\nB. $\\sqrt{\\frac{2 k T}{m}}$\n\nC. $\\sqrt{\\frac{3 k T}{m}}$\n\nD. $\\sqrt{\\frac{8 k T}{\\pi m}}$\n\nE. $\\frac{k T}{m}$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "The energy from electromagnetic waves in equilibrium in a cavity is used to melt ice. If the Kelvin temperature of the cavity is increased by a factor of two, the mass of ice that can be melted in a fixed amount of time is increased by a factor of\n\nA. 2\n\nB. 4\n\nC. 8\n\nD. 16\n\nE. 32\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "The figure above represents the orbit of a planet around a star, $S$, and the marks divide the orbit into 14 equal time intervals, $t=T / 14$, where $T$ is the orbital period. If the only force acting on the planet is Newtonian gravitation, then true statements about the situation include which of the following?\n\nI. Area $A=\\operatorname{area} B$\n\nII. The star $S$ is at one focus of an elliptically shaped orbit.\n\nIII. $T^{2}=C a^{3}$, where $a$ is the semimajor axis of the ellipse and $C$ is a constant.\n\nA. I only\n\nB. II only\n\nC. I and II only\n\nD. II and III only\n\nE. I, II, and III\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "A massless spring with force constant $k$ launches a ball of mass $m$. In order for the ball to reach a speed $v$, by what displacement $s$ should the spring be compressed?\n\nA. $s=v \\sqrt{\\frac{k}{m}}$\n\nB. $s=v \\sqrt{\\frac{m}{k}}$\n\nC. $s=v \\sqrt{\\frac{2 k}{m}}$\n\nD. $s=v \\frac{m}{k}$\n\nE. $s=v^{2} \\frac{m}{2 k}$", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A quantum mechanical harmonic oscillator has an angular frequency $\\omega$. The Schrödinger equation predicts that the ground state energy of the oscillator will be\n\nA. $-\\frac{1}{2} \\hbar \\omega$\n\nB. 0\n\nC. $\\frac{1}{2} \\hbar \\omega$\n\nD. $\\hbar \\omega$\n\nE. $\\frac{3}{2} \\hbar \\omega$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "In the Bohr model of the hydrogen atom, the linear momentum of the electron at radius $r_{n}$ is given by which of the following? ( $n$ is the principal quantum number.)\n\nA. $n \\hbar$\n\nB. $n r_{n} \\hbar$\n\nC. $\\frac{n \\hbar}{r_{n}}$\n\nD. $n^{2} r_{n} \\hbar$\n\nE. $\\frac{n^{2} \\hbar}{r_{n}}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "The figure above represents a log-log plot of variable $y$ versus variable $x$. The origin represents the point $x=1$ and $y=1$. Which of the following gives the approximate functional relationship between $y$ and $x$ ?\n\nA. $y=6 \\sqrt{x}$\n\nB. $y=\\frac{1}{2} x+6$\n\nC. $y=6 x+0.5$\n\nD. $y=\\frac{1}{6} x^{2}$\n\nE. $y=6 x^{2}$\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "Two experimental techniques determine the mass of an object to be $11 \\pm 1 \\mathrm{~kg}$ and $10 \\pm 2 \\mathrm{~kg}$. These two measurements can be combined to give a weighted average. The uncertainty of the weighted average is equal to which of the following?\n\nA. $\\frac{1}{2} \\mathrm{~kg}$\n\nB. $\\frac{2}{\\sqrt{5}} \\mathrm{~kg}$\n\nC. $\\frac{2}{\\sqrt{3}} \\mathrm{~kg}$\n\nD. $2 \\mathrm{~kg}$\n\nE. $\\sqrt{5} \\mathrm{~kg}$", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "If the five lenses shown below are made of the same material, which lens has the shortest positive focal length?\n\nA.\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "Unpolarized light is incident on a pair of ideal linear polarizers whose transmission axes make an angle of $45^{\\circ}$ with each other. The transmitted light intensity through both polarizers is what percentage of the incident intensity?\n\nA. $100 \\%$\n\nB. $75 \\%$\n\nC. $50 \\%$\n\nD. $25 \\%$\n\nE. $0 \\%$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "A very long, thin, straight wire carries a uniform charge density of $\\lambda$ per unit length. Which of the following gives the magnitude of the electric field at a radial distance $r$ from the wire?\n\nA. $\\frac{1}{2 \\pi \\varepsilon_{0}} \\frac{\\lambda}{r}$\n\nB. $\\frac{1}{2 \\pi \\varepsilon_{0}} \\frac{r}{\\lambda}$\n\nC. $\\frac{1}{2 \\pi \\varepsilon_{0}} \\frac{\\lambda}{r^{2}}$\n\nD. $\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{\\lambda^{2}}{r^{2}}$\n\nE. $\\frac{1}{4 \\pi \\varepsilon_{0}} \\lambda \\ln r$\n\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "The bar magnet shown in the figure above is moved completely through the loop. Which of the following is a true statement about the direction of the current flow between the two points $a$ and $b$ in the circuit?\n\nA. No current flows between $a$ and $b$ as the magnet passes through the loop.\n\nB. Current flows from $a$ to $b$ as the magnet passes through the loop.\n\nC. Current flows from $b$ to $a$ as the magnet passes through the loop.\n\nD. Current flows from $a$ to $b$ as the magnet enters the loop and from $b$ to $a$ as the magnet leaves the loop.\n\nE. Current flows from $b$ to $a$ as the magnet enters the loop and from $a$ to $b$ as the magnet leaves the loop.\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "The surface of the Sun has a temperature close to $6,000 \\mathrm{~K}$ and it emits a blackbody (Planck) spectrum that reaches a maximum near $500 \\mathrm{~nm}$. For a body with a surface temperature close to $300 \\mathrm{~K}$, at what wavelength would the thermal spectrum reach a maximum?\n\nA. $10 \\mu \\mathrm{m}$\n\nB. $100 \\mu \\mathrm{m}$\n\nC. $10 \\mathrm{~mm}$\n\nD. $100 \\mathrm{~mm}$\n\nE. $10 \\mathrm{~m}$\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "At the present time, the temperature of the universe (i.e., the microwave radiation background) is about $3 \\mathrm{~K}$. When the temperature was $12 \\mathrm{~K}$, typical objects in the universe, such as galaxies, were\n\nA. one-quarter as distant as they are today\n\nB. one-half as distant as they are today\n\nC. separated by about the same distances as they are today\n\nD. two times as distant as they are today\n\nE. four times as distant as they are today\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "For an adiabatic process involving an ideal gas having volume $V$ and temperature $T$, which of the following is constant? $\\left(\\gamma=C_{P} / C_{V}\\right)$\n\nA. $T V$\n\nB. $T V^{\\gamma}$\n\nC. $T V^{\\gamma-1}$\n\nD. $T^{\\gamma} V$\n\nE. $T^{\\gamma} V^{-1}$", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "An electron has total energy equal to four times its rest energy. The momentum of the electron is\n\nA. $m_{e} c$\n\nB. $\\sqrt{2} m_{e} c$\n\nC. $\\sqrt{15} m_{e} c$\n\nD. $4 m_{e} c$\n\nE. $2 \\sqrt{15} m_{e} c$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "Two spaceships approach Earth with equal speeds, as measured by an observer on Earth, but from opposite directions. A meterstick on one spaceship is measured to be $60 \\mathrm{~cm}$ long by an occupant of the other spaceship. What is the speed of each spaceship, as measured by the observer on Earth?\n\nA. $0.4 c$\n\nB. $0.5 c$\n\nC. $0.6 c$\n\nD. $0.7 c$\n\nE. $0.8 c$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A meter stick with a speed of $0.8 c$ moves past an observer. In the observer's reference frame, how long does it take the stick to pass the observer?\n\nA. $1.6 \\mathrm{~ns}$\n\nB. $2.5 \\mathrm{~ns}$\n\nC. $4.2 \\mathrm{~ns}$\n\nD. $6.9 \\mathrm{~ns}$\n\nE. $8.3 \\mathrm{~ns}$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "Consider a set of wave functions $\\psi_{i}(x)$. Which of the following conditions guarantees that the functions are normalized and mutually orthogonal? (The indices $i$ and $j$ take on the values in the set $\\{1,2, \\ldots, n\\}$. )\n\nA. $\\psi_{i}^{*}(x) \\psi_{j}(x)=0$\n\nB. $\\psi_{i}^{*}(x) \\psi_{j}(x)=1$\n\nC. $\\int_{-\\infty}^{\\infty} \\psi_{i}^{*}(x) \\psi_{j}(x) d x=0$\n\nD. $\\int_{-\\infty}^{\\infty} \\psi_{i}^{*}(x) \\psi_{j}(x) d x=1$\n\nE. $\\int_{-\\infty}^{\\infty} \\psi_{i}^{*}(x) \\psi_{j}(x) d x=\\delta_{i j}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "The normalized ground state wave function of hydrogen is $\\psi_{100}=\\frac{2}{(4 \\pi)^{1 / 2} a_{0}^{3 / 2}} e^{-r / a_{0}}$, where $a_{0}$ is the Bohr radius. What is the most likely distance that the electron is from the nucleus?\n\nA. 0\n\nB. $\\frac{a_{0}}{2}$\n\nC. $\\frac{a_{0}}{\\sqrt{2}}$\n\nD. $a_{0}$\n\nE. $2 a_{0}$", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "The lifetime for the $2 p \\rightarrow 1 s$ transition in hydrogen is $1.6 \\times 10^{-9} \\mathrm{~s}$. The natural line width for the radiation emitted during the transition is approximately\n\nA. $100 \\mathrm{~Hz}$\n\nB. $100 \\mathrm{kHz}$\n\nC. $100 \\mathrm{MHz}$\n\nD. $100 \\mathrm{GHz}$\n\nE. $100 \\mathrm{THz}$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "A spring of force constant $k$ is stretched a certain distance. It takes twice as much work to stretch a second spring by half this distance. The force constant of the second spring is\n\nA. $k$\n\nB. $2 k$\n\nC. $4 k$\n\nD. $8 k$\n\nE. $16 k$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "On a frictionless surface, a block of mass $M$ moving at speed $v$ collides elastically with another block of the same mass that is initially at rest. After the collision, the first block moves at an angle $\\theta$ to its initial direction and has a speed $v / 2$. The second block's speed after the collision is\n\nA. $\\frac{\\sqrt{3}}{4} v$\n\nB. $\\frac{v}{2}$\n\nC. $\\frac{\\sqrt{3}}{2} v$\n\nD. $\\frac{\\sqrt{5}}{2} v$\n\nE. $v+\\frac{v}{2} \\cos \\theta$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "Which of the following gives Hamilton's canonical equation(s) of motion? ( $H$ is the Hamiltonian, $q_{i}$ are the generalized coordinates, and $p_{i}$ are the generalized momenta.)\n\nA. $q_{i}=\\frac{\\partial H}{\\partial p_{i}}, \\quad p_{i}=-\\frac{\\partial H}{\\partial q_{i}}$\n\nB. $q_{i}=\\frac{\\partial H}{\\partial \\dot{q}_{i}}, \\quad p_{i}=\\frac{\\partial H}{\\partial \\dot{p}_{i}}$\n\nC. $\\dot{q}_{i}=\\frac{\\partial H}{\\partial q_{i}}, \\quad \\dot{p}_{i}=-\\frac{\\partial H}{\\partial p_{i}}$\n\nD. $\\dot{q}_{i}=\\frac{\\partial H}{\\partial p_{i}}, \\quad \\dot{p}_{i}=-\\frac{\\partial H}{\\partial q_{i}}$\n\nE. $\\frac{d}{d t}\\left(\\frac{\\partial H}{\\partial p_{i}}\\right)-\\frac{\\partial H}{\\partial q_{i}}=0$\n\n\\begin{tabular}{|l|}\n\\hline Oil \\\\\n\\hline Water \\\\\n\\hline\n\\end{tabular}\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "A layer of oil with density $800 \\mathrm{~kg} / \\mathrm{m}^{3}$ floats on top of a volume of water with density $1,000 \\mathrm{~kg} / \\mathrm{m}^{3}$. A block floats at the oil-water interface with $1 / 4$ of its volume in oil and 3/4 of its volume in water, as shown in the figure above. What is the density of the block?\n\nA. $200 \\mathrm{~kg} / \\mathrm{m}^{3}$\n\nB. $850 \\mathrm{~kg} / \\mathrm{m}^{3}$\n\nC. $950 \\mathrm{~kg} / \\mathrm{m}^{3}$\n\nD. $1,050 \\mathrm{~kg} / \\mathrm{m}^{3}$\n\nE. $1,800 \\mathrm{~kg} / \\mathrm{m}^{3}$", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": true}
{"input": "An incompressible fluid of density $\\rho$ flows through a horizontal pipe of radius $r$ and then passes through a constriction of radius $r / 2$. If the fluid has pressure $P_{0}$ and velocity $v_{0}$ before the constriction, the pressure in the constriction is\n\nA. $P_{0}-\\frac{15}{2} \\rho v_{0}^{2}$\n\nB. $P_{0}-\\frac{3}{2} \\rho v_{0}^{2}$\n\nC. $\\frac{P_{0}}{4}$\n\nD. $P_{0}+\\frac{3}{2} \\rho v_{0}^{2}$\n\nE. $P_{0}+\\frac{15}{2} \\rho v_{0}^{2}$\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A thermodynamic system, initially at absolute temperature $T_{1}$, contains a mass $m$ of water with specific heat capacity $c$. Heat is added until the temperature rises to $T_{2}$. The change in entropy of the water is\n\nA. 0\n\nB. $T_{2}-T_{1}$\n\nC. $m c T_{2}$\n\nD. $m c\\left(T_{2}-T_{1}\\right)$\n\nE. $m c \\ln \\left(\\frac{T_{2}}{T_{1}}\\right)$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "Heat $Q$ is added to a monatomic ideal gas under conditions of constant volume, resulting in a temperature change $\\Delta T$. How much heat will be required to produce the same temperature change, if it is added under conditions of constant pressure?\n\nA. $\\frac{3}{5} Q$\n\nB. $Q$\n\nC. $\\frac{5}{3} Q$\n\nD. $2 Q$\n\nE. $\\frac{10}{3} Q$", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "A heat pump is to extract heat from an outdoor environment at $7^{\\circ} \\mathrm{C}$ and heat the environment indoors to $27^{\\circ} \\mathrm{C}$. For each $15,000 \\mathrm{~J}$ of heat delivered indoors, the smallest amount of work that must be supplied to the heat pump is approximately\n\nA. $500 \\mathrm{~J}$\n\nB. $1,000 \\mathrm{~J}$\n\nC. $1,100 \\mathrm{~J}$\n\nD. $2,000 \\mathrm{~J}$\n\nE. $2,200 \\mathrm{~J}$\n\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "The capacitor in the circuit above is charged. If switch $S$ is closed at time $t=0$, which of the following represents the magnetic energy, $U$, in the inductor as a function of time? (Assume that the capacitor and inductor are ideal.)\n\nA.\n\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "A pair of electric charges of equal magnitude $q$ and opposite sign are separated by a distance $\\ell$, as shown in the figure above. Which of the following gives the approximate magnitude and direction of the electric field set up by the two charges at a point $P$ on the $y$-axis, which is located a distance $r \\gg \\ell$ from the $x$-axis?\nMagnitude\nDirection\nA. $\\frac{1}{4 \\pi \\epsilon_{0}} \\frac{2 q}{r^{2}}$\n$+y$\nB. $\\frac{1}{4 \\pi \\epsilon_{0}} \\frac{2 q}{r^{2}}$\n$+x$\nC. $\\frac{1}{4 \\pi \\epsilon_{0}} \\frac{2 q}{r^{2}}$\n$-x$\nD. $\\frac{1}{4 \\pi \\epsilon_{0}} \\frac{q \\ell}{r^{3}}$\n$+x$\nE. $\\frac{1}{4 \\pi \\epsilon_{0}} \\frac{q \\ell}{r^{3}}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "Consider two very long, straight, insulated wires oriented at right angles. The wires carry currents of equal magnitude $I$ in the directions shown in the figure above. What is the net magnetic field at point $P$ ?\n\nA. $\\frac{\\mu_{0} I}{2 \\pi a}(\\hat{\\mathbf{x}}+\\hat{\\mathbf{y}})$\n\nB. $-\\frac{\\mu_{0} I}{2 \\pi a}(\\hat{\\mathbf{x}}+\\hat{\\mathbf{y}})$\n\nC. $\\frac{\\mu_{0} I}{\\pi a} \\hat{\\mathbf{z}}$\n\nD. $-\\frac{\\mu_{0} I}{\\pi a} \\hat{\\mathbf{z}}$\n\nE. 0\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "A beam of muons travels through the laboratory with speed $v=\\frac{4}{5} c$. The lifetime of a muon in its rest frame is $\\tau=2.2 \\times 10^{-6} \\mathrm{~s}$. The mean distance traveled by the muons in the laboratory frame is\n\nA. $530 \\mathrm{~m}$\n\nB. $660 \\mathrm{~m}$\n\nC. $880 \\mathrm{~m}$\n\nD. $1,100 \\mathrm{~m}$\n\nE. $1,500 \\mathrm{~m}$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "A particle of mass $M$ decays from rest into two particles. One particle has mass $m$ and the other particle is massless. The momentum of the massless particle is\n\nA. $\\frac{\\left(M^{2}-m^{2}\\right) c}{4 M}$\n\nB. $\\frac{\\left(M^{2}-m^{2}\\right) c}{2 M}$\n\nC. $\\frac{\\left(M^{2}-m^{2}\\right) c}{M}$\n\nD. $\\frac{2\\left(M^{2}-m^{2}\\right) c}{M}$\n\nE. $\\frac{4\\left(M^{2}-m^{2}\\right) c}{M}$\n\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "In an experimental observation of the photoelectric effect, the stopping potential was plotted versus the light frequency, as shown in the figure above. The best straight line was fitted to the experimental points. Which of the following gives the slope of the line? (The work function of the metal is $\\phi$.)\n\nA. $\\frac{h}{\\phi}$\n\nB. $\\frac{h}{e}$\n\nC. $\\frac{e}{h}$\n\nD. $\\frac{e}{\\phi}$\n\nE. $\\frac{\\phi}{e}$\n\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": true}
{"input": "Two sinusoidal waveforms of the same frequency are displayed on an oscilloscope screen, as indicated above. The horizontal sweep of the oscilloscope is set to $100 \\mathrm{~ns} / \\mathrm{cm}$ and the vertical gains of channels 1 and 2 are each set to $2 \\mathrm{~V} / \\mathrm{cm}$. The zero-voltage level of each channel is given at the right in the figure. The phase difference between the two waveforms is most nearly\n\nA. $30^{\\circ}$\n\nB. $45^{\\circ}$\n\nC. $60^{\\circ}$\n\nD. $90^{\\circ}$\n\nE. $120^{\\circ}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": true}
{"input": "In the diamond structure of elemental carbon, the nearest neighbors of each $\\mathrm{C}$ atom lie at the corners of a\n\nA. square\n\nB. hexagon\n\nC. cube\n\nD. tetrahedron\n\nE. octahedron", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "According to the BCS theory, the attraction between Cooper pairs in a superconductor is due to\n\nA. the weak nuclear force\n\nB. the strong nuclear force\n\nC. vacuum polarization\n\nD. interactions with the ionic lattice\n\nE. the Casimir effect\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "During a hurricane, a $1,200 \\mathrm{~Hz}$ warning siren on the town hall sounds. The wind is blowing at $55 \\mathrm{~m} / \\mathrm{s}$ in a direction from the siren toward a person $1 \\mathrm{~km}$ away. With what frequency does the sound wave reach the person? (The speed of sound in air is $330 \\mathrm{~m} / \\mathrm{s}$.)\n\nA. $1,000 \\mathrm{~Hz}$\n\nB. $1,030 \\mathrm{~Hz}$\n\nC. $1,200 \\mathrm{~Hz}$\n\nD. $1,400 \\mathrm{~Hz}$\n\nE. $1,440 \\mathrm{~Hz}$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "Sound waves moving at $350 \\mathrm{~m} / \\mathrm{s}$ diffract out of a speaker enclosure with an opening that is a long rectangular slit $0.14 \\mathrm{~m}$ across. At about what frequency will the sound first disappear at an angle of $45^{\\circ}$ from the normal to the speaker face?\n\nA. $500 \\mathrm{~Hz}$\n\nB. $1,750 \\mathrm{~Hz}$\n\nC. $2,750 \\mathrm{~Hz}$\n\nD. $3,500 \\mathrm{~Hz}$\n\nE. $5,000 \\mathrm{~Hz}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "An organ pipe, closed at one end and open at the other, is designed to have a fundamental frequency of $\\mathrm{C}(131 \\mathrm{~Hz})$. What is the frequency of the next higher harmonic for this pipe?\n\nA. $44 \\mathrm{~Hz}$\n\nB. $196 \\mathrm{~Hz}$\n\nC. $262 \\mathrm{~Hz}$\n\nD. $393 \\mathrm{~Hz}$\n\nE. $524 \\mathrm{~Hz}$\n\nInputs\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "For the logic circuit shown above, which of the following Boolean statements gives the output $E$ in terms of inputs $A, B, C$, and $D$ ?\n\nA. $E=\\overline{A+B}+\\overline{C \\cdot D}$\n\nB. $E=\\overline{A+B} \\cdot \\overline{C \\cdot D}$\n\nC. $E=\\overline{\\bar{A}+\\bar{B}} \\cdot \\overline{C \\cdot D}$\n\nD. $E=\\overline{A \\cdot B} \\cdot \\overline{C \\cdot D}$\n\nE. $E=\\overline{\\bar{A} \\cdot \\bar{B}} \\cdot \\overline{C \\cdot D}$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": true}
{"input": "Which of the following lasers utilizes transitions that involve the energy levels of free atoms?\n\nA. Diode laser\n\nB. Dye laser\n\nC. Free-electron laser\n\nD. Gas laser\n\nE. Solid-state laser", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "Which of the following expressions is proportional to the total energy for the levels of a oneelectron Bohr atom? ( $m$ is the reduced mass, $Z$ is the number of protons in the nucleus, $-e$ is the charge on the electron, and $n$ is the principal quantum number.)\n\nA. $\\frac{m Z e^{2}}{n}$\n\nB. $\\frac{m Z e^{2}}{n^{2}}$\n\nC. $\\frac{m Z^{2} e^{4}}{n^{2}}$\n\nD. $\\frac{m^{2} Z^{2} e^{2}}{n^{2}}$\n\nE. $\\frac{m^{2} Z^{2} e^{4}}{n^{2}}$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "True statements about the absorption and emission of energy by an atom include which of the following?\n\nI. An atom can only absorb photons of light that have certain specific energies.\n\nII. An atom can emit photons of light of any energy.\n\nIII. At low temperature, the lines in the absorption spectrum of an atom coincide with the lines in its emission spectrum that represent transitions to the ground state.\n\nA. I only\n\nB. III only\n\nC. I and II only\n\nD. I and III only\n\nE. I, II, and III\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "$X$ rays of wavelength $\\lambda=0.250 \\mathrm{~nm}$ are incident on the face of a crystal at angle $\\theta$, measured from the crystal surface. The smallest angle that yields an intense reflected beam is $\\theta=14.5^{\\circ}$. Which of the following gives the value of the interplanar spacing $d ?\\left(\\sin 14.5^{\\circ} \\approx 1 / 4\\right)$\n\nA. $0.125 \\mathrm{~nm}$\n\nB. $0.250 \\mathrm{~nm}$\n\nC. $0.500 \\mathrm{~nm}$\n\nD. $0.625 \\mathrm{~nm}$\n\nE. $0.750 \\mathrm{~nm}$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "Astronomers observe two separate solar systems, each consisting of a planet orbiting a sun. The two orbits are circular and have the same radius $R$. It is determined that the planets have angular momenta of the same magnitude $L$ about their suns, and that the orbital periods are in the ratio of three to one; i.e., $T_{1}=3 T_{2}$. The ratio $m_{1} / m_{2}$ of the masses of the two planets is\n\nA. 1\n\nB. $\\sqrt{3}$\n\nC. 2\n\nD. 3\n\nE. 9\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "If the Sun were suddenly replaced by a black hole of the same mass, it would have a Schwarzschild radius of $3,000 \\mathrm{~m}$. What effect, if any, would this change have on the orbits of the planets?\n\nA. The planets would move directly toward the Sun.\n\nB. The planets would move in spiral orbits.\n\nC. The planets would oscillate about their former elliptical orbits.\n\nD. The orbits would precess much more rapidly.\n\nE. The orbits would remain unchanged.", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "A distant galaxy is observed to have its hydrogen- $\\beta$ line shifted to a wavelength of $580 \\mathrm{~nm}$, away from the laboratory value of $434 \\mathrm{~nm}$. Which of the following gives the approximate velocity of recession of the distant galaxy? (Note: $\\frac{580}{434} \\approx \\frac{4}{3}$ )\n\nA. $0.28 c$\n\nB. $0.53 c$\n\nC. $0.56 c$\n\nD. $0.75 c$\n\nE. $0.86 c$\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A small plane can fly at a speed of $200 \\mathrm{~km} / \\mathrm{h}$ in still air. A $30 \\mathrm{~km} / \\mathrm{h}$ wind is blowing from west to east. How much time is required for the plane to fly $500 \\mathrm{~km}$ due north?\n\nA. $\\frac{50}{23} \\mathrm{~h}$\n\nB. $\\frac{50}{\\sqrt{409}} \\mathrm{~h}$\n\nC. $\\frac{50}{20} \\mathrm{~h}$\n\nD. $\\frac{50}{\\sqrt{391}} \\mathrm{~h}$\n\nE. $\\frac{50}{17} \\mathrm{~h}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "Each of the figures above shows blocks of mass $2 m$ and $m$ acted on by an external horizontal force $\\mathbf{F}$. For each figure, which of the following statements about the magnitude of the force that one block exerts on the other $\\left(F_{12}\\right)$ is correct? (Assume that the surface on which the blocks move is frictionless.)\n\n\\section*{Figure 1}\n\nA. $F_{12}=\\frac{F}{3}$\n\nB. $F_{12}=\\frac{F}{3}$\n\nC. $F_{12}=\\frac{2 F}{3}$\n\nD. $F_{12}=\\frac{2 F}{3}$\n\nE. $F_{12}=F$\n\n\\section*{Figure 2}\n\n$$\nF_{12}=\\frac{F}{3}\n$$\n\n$F_{12}=\\frac{2 F}{3}$\n\n$F_{12}=\\frac{F}{3}$\n\n$F_{12}=\\frac{2 F}{3}$\n\n$F_{12}=F$\n\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "In the figure above, block $A$ has mass\n\n$m_{A}=25 \\mathrm{~kg}$ and block $B$ has mass $m_{B}=10 \\mathrm{~kg}$.\n\nBoth blocks move with constant acceleration $a=2 \\mathrm{~m} / \\mathrm{s}^{2}$ to the right, and the coefficient of static friction between the two blocks is $\\mu_{s}=0.8$. The static frictional force acting between the blocks is\n\nA. $20 \\mathrm{~N}$\n\nB. $50 \\mathrm{~N}$\n\nC. $78 \\mathrm{~N}$\n\nD. $196 \\mathrm{~N}$\n\nE. $274 \\mathrm{~N}$\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A simple pendulum of length $l$ is suspended from the ceiling of an elevator that is accelerating upward with constant acceleration $a$. For small oscillations, the period, $T$, of the pendulum is\n\nA. $T=2 \\pi \\sqrt{\\frac{l}{g}}$\n\nB. $T=2 \\pi \\sqrt{\\frac{l}{g-a}}$\n\nC. $T=2 \\pi \\sqrt{\\frac{l}{g+a}}$\n\nD. $T=2 \\pi \\sqrt{\\frac{l}{g} \\frac{a}{(g+a)}}$\n\nE. $T=2 \\pi \\sqrt{\\frac{l}{g} \\frac{(g+a)}{a}}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "Three long, straight wires in the $x z$-plane, each carrying current $I$, cross at the origin of coordinates, as shown in the figure above. Let $\\hat{\\mathbf{x}}, \\hat{\\mathbf{y}}$, and $\\hat{\\mathbf{z}}$ denote the unit vectors in the $x$-, $y$-, and $z$-directions, respectively. The magnetic field $\\mathbf{B}$ as a function of $x$, with $y=0$ and $z=0$, is\n\nA. $\\mathbf{B}=\\frac{3 \\mu_{0} I}{2 \\pi x} \\hat{\\mathbf{x}}$\n\nB. $\\mathbf{B}=\\frac{3 \\mu_{0} I}{2 \\pi x} \\hat{\\mathbf{y}}$\n\nC. $\\mathbf{B}=\\frac{\\mu_{0} I}{2 \\pi x}(1+2 \\sqrt{2}) \\hat{\\mathbf{y}}$\n\nD. $\\mathbf{B}=\\frac{\\mu_{0} I}{2 \\pi x} \\hat{\\mathbf{x}}$\n\nE. $\\mathbf{B}=\\frac{\\mu_{0} I}{2 \\pi x} \\hat{\\mathbf{y}}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "A particle with mass $m$ and charge $q$, moving with a velocity $\\mathbf{v}$, enters a region of uniform magnetic field $\\mathbf{B}$, as shown in the figure above. The particle strikes the wall at a distance $d$ from the entrance slit. If the particle's velocity stays the same but its charge-to-mass ratio is doubled, at what distance from the entrance slit will the particle strike the wall?\n\nA. $2 d$\n\nB. $\\sqrt{2} d$\n\nC. $d$\n\nD. $\\frac{1}{\\sqrt{2}} d$\n\nE. $\\frac{1}{2} d$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "Consider the closed cylindrical Gaussian surface above. Suppose that the net charge enclosed within this surface is $+1 \\times 10^{-9} \\mathrm{C}$ and the electric flux out through the portion of the surface marked $A$ is $-100 \\mathrm{~N} \\cdot \\mathrm{m}^{2} / \\mathrm{C}$. The flux through the rest of the surface is most nearly given by which of the following?\n\nA. $-100 \\mathrm{~N} \\cdot \\mathrm{m}^{2} / \\mathrm{C}$\n\nB. $\\quad 0 \\mathrm{~N} \\cdot \\mathrm{m}^{2} / \\mathrm{C}$\n\nC. $10 \\mathrm{~N} \\cdot \\mathrm{m}^{2} / \\mathrm{C}$\n\nD. $100 \\mathrm{~N} \\cdot \\mathrm{m}^{2} / \\mathrm{C}$\n\nE. $200 \\mathrm{~N} \\cdot \\mathrm{m}^{2} / \\mathrm{C}$\n\n$$\n{ }^{13} \\mathrm{~N} \\rightarrow{ }^{13} \\mathrm{C}+e^{+}+v_{e}\n$$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "The nuclear decay above is an example of a process induced by the\n\nA. Mössbauer effect\n\nB. Casimir effect\n\nC. photoelectric effect\n\nD. weak interaction\n\nE. strong interaction\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "Consider a single electron atom with orbital angular momentum $L=\\sqrt{2} \\hbar$. Which of the following gives the possible values of a measurement of $L_{z}$, the $z$-component of $L$ ?\n\nA. 0\n\nB. $0, \\hbar$\n\nC. $0, \\hbar, 2 \\hbar$\n\nD. $-\\hbar, 0, \\hbar$\n\nE. $-2 \\hbar,-\\hbar, 0, \\hbar, 2 \\hbar$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "Characteristics of the quantum harmonic oscillator include which of the following?\n\nI. A spectrum of evenly spaced energy states\n\nII. A potential energy function that is linear in the position coordinate\n\nIII. A ground state that is characterized by zero kinetic energy\n\nIV. A nonzero probability of finding the oscillator outside the classical turning points\n\nA. I only\n\nB. IV only\n\nC. I and IV only\n\nD. II and III only\n\nE. I, II, III, and IV", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "A muon can be considered to be a heavy electron with a mass $m_{\\mu}=207 m_{e}$. Imagine replacing the electron in a hydrogen atom with a muon. What are the energy levels $E_{n}$ for this new form of hydrogen in terms of the binding energy of ordinary hydrogen $E_{0}$, the mass of the proton $m_{p}$, and the principal quantum number $n$ ?\n\nA. $E_{n}=\\frac{-E_{0}}{n^{2}}\\left(\\frac{m_{\\mu}}{m_{e}}\\right)$\n\nB. $E_{n}=\\frac{-E_{0}}{n^{2}}\\left(\\frac{m_{e}}{m_{\\mu}}\\right)$\n\nC. $E_{n}=\\frac{-E_{0}}{n^{2}}\\left(\\frac{\\left(m_{p}+m_{e}\\right)}{\\left(m_{p}+m_{\\mu}\\right)}\\right)$\n\nD. $E_{n}=\\frac{-E_{0}}{n^{2}}\\left(\\frac{m_{\\mu}\\left(m_{p}+m_{e}\\right)}{m_{e}\\left(m_{p}+m_{\\mu}\\right)}\\right)$\n\nE. $E_{n}=\\frac{-E_{0}}{n^{2}}\\left(\\frac{m_{e}\\left(m_{p}+m_{\\mu}\\right)}{m_{\\mu}\\left(m_{p}+m_{e}\\right)}\\right)$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "A large, parallel-plate capacitor consists of two square plates that measure $0.5 \\mathrm{~m}$ on each side. A charging current of $9 \\mathrm{~A}$ is applied to the capacitor. Which of the following gives the approximate rate of change of the electric field between the plates?\n\nA. $2 \\frac{\\mathrm{V}}{\\mathrm{m} \\cdot \\mathrm{s}}$\n\nB. $40 \\frac{\\mathrm{V}}{\\mathrm{m} \\cdot \\mathrm{s}}$\n\nC. $1 \\times 10^{12} \\frac{\\mathrm{V}}{\\mathrm{m} \\cdot \\mathrm{s}}$\n\nD. $4 \\times 10^{12} \\frac{\\mathrm{V}}{\\mathrm{m} \\cdot \\mathrm{s}}$\n\nE. $2 \\times 10^{13} \\frac{\\mathrm{V}}{\\mathrm{m} \\cdot \\mathrm{s}}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "The circuit shown in the figure above consists of eight resistors, each with resistance $R$, and a battery with terminal voltage $V$ and negligible internal resistance. What is the current flowing through the battery?\n\nA. $\\frac{1}{3} \\frac{V}{R}$\n\nB. $\\frac{1}{2} \\frac{V}{R}$\n\nC. $\\frac{V}{R}$\n\nD. $\\frac{3}{2} \\frac{V}{R}$\n\nE. $3 \\frac{V}{R}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "In the AC circuit above, $V_{i}$ is the amplitude of the input voltage and $V_{o}$ is the amplitude of the output voltage. If the angular frequency $\\omega$ of the input voltage is varied, which of the following gives the ratio $V_{o} / V_{i}=G$ as a function of $\\omega$ ?\n\nA.\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "A wire loop that encloses an area of $10 \\mathrm{~cm}^{2}$ has a resistance of $5 \\Omega$. The loop is placed in a magnetic field of $0.5 \\mathrm{~T}$ with its plane perpendicular to the field. The loop is suddenly removed from the field. How much charge flows past a given point in the wire?\n\nA. $10^{-4} \\mathrm{C}$\n\nB. $10^{-3} \\mathrm{C}$\n\nC. $10^{-2} \\mathrm{C}$\n\nD. $10^{-1} \\mathrm{C}$\n\nE. $1 \\mathrm{C}$\n\n", "target_scores": {"A": 1, "B": 0, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "Two nonrelativistic electrons move in circles under the influence of a uniform magnetic field $\\mathbf{B}$, as shown in the figure above. The ratio $r_{1} / r_{2}$ of the orbital radii is equal to $1 / 3$. Which of the following is equal to the ratio $v_{1} / v_{2}$ of the speeds?\n\nA. $1 / 9$\n\nB. $1 / 3$\n\nC. 1\n\nD. 3\n\nE. 9", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "Which of the following statements about bosons and/or fermions is true?\n\nA. Bosons have symmetric wave functions and obey the Pauli exclusion principle.\n\nB. Bosons have antisymmetric wave functions and do not obey the Pauli exclusion principle.\n\nC. Fermions have symmetric wave functions and obey the Pauli exclusion principle.\n\nD. Fermions have antisymmetric wave functions and obey the Pauli exclusion principle.\n\nE. Bosons and fermions obey the Pauli exclusion principle.\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "The discovery of the $J / \\psi$ particle was especially significant because it provided evidence for which of the following?\n\nA. Parity violation in weak interactions\n\nB. Massive neutrinos\n\nC. Higgs bosons\n\nD. Charmed quarks\n\nE. Strange quarks\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "The figure above shows an object $O$ placed at a distance $R$ to the left of a convex spherical mirror that has a radius of curvature $R$. Point $C$ is the center of curvature of the mirror. The image formed by the mirror is at\n\nA. infinity\n\nB. a distance $R$ to the left of the mirror and inverted\n\nC. a distance $R$ to the right of the mirror and upright\n\nD. a distance $\\frac{R}{3}$ to the left of the mirror and inverted\n\nE. a distance $\\frac{R}{3}$ to the right of the mirror and upright\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "A uniform thin film of soapy water with index of refraction $n=1.33$ is viewed in air via reflected light. The film appears dark for long wavelengths and first appears bright for $\\lambda=540 \\mathrm{~nm}$. What is the next shorter wavelength at which the film will appear bright on reflection?\n\nA. $135 \\mathrm{~nm}$\n\nB. $180 \\mathrm{~nm}$\n\nC. $270 \\mathrm{~nm}$\n\nD. $320 \\mathrm{~nm}$\n\nE. $405 \\mathrm{~nm}$\n\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A model of an optical fiber is shown in the figure above. The optical fiber has an index of refraction, $n$, and is surrounded by free space. What angles of incidence, $\\theta$, will result in the light staying in the optical fiber?\n\nA. $\\theta>\\sin ^{-1}\\left(\\sqrt{n^{2}-1}\\right)$\n\nB. $\\theta<\\sin ^{-1}\\left(\\sqrt{n^{2}-1}\\right)$\n\nC. $\\theta>\\sin ^{-1}\\left(\\sqrt{n^{2}+1}\\right)$\n\nD. $\\theta<\\sin ^{-1}\\left(\\sqrt{n^{2}+1}\\right)$\n\nE. $\\sin ^{-1}\\left(\\sqrt{n^{2}-1}\\right)<\\theta<\\sin ^{-1}\\left(\\sqrt{n^{2}+1}\\right)$", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A gas at temperature $T$ is composed of molecules of mass $m$. Which of the following describes how the average time between intermolecular collisions varies with $m$ ?\n\nA. It is proportional to $\\frac{1}{m}$.\n\nB. It is proportional to $\\sqrt[4]{m}$.\n\nC. It is proportional to $\\sqrt{m}$.\n\nD. It is proportional to $m$.\n\nE. It is proportional to $m^{2}$.\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "A particle can occupy two possible states with energies $E_{1}$ and $E_{2}$, where $E_{2}>E_{1}$. At temperature $T$, the probability of finding the particle in state 2 is given by which of the following?\n\nA. $\\frac{\\mathrm{e}^{-E_{1} / k T}}{\\mathrm{e}^{-E_{1} / k T}+\\mathrm{e}^{-E_{2} / k T}}$\n\nB. $\\frac{\\mathrm{e}^{-E_{2} / k T}}{\\mathrm{e}^{-E_{1} / k T}+\\mathrm{e}^{-E_{2} / k T}}$\n\nC. $\\frac{\\mathrm{e}^{-\\left(E_{1}+E_{2}\\right) / k T}}{\\mathrm{e}^{-E_{1} / k T}+\\mathrm{e}^{-E_{2} / k T}}$\n\nD. $\\frac{\\mathrm{e}^{-E_{1} / k T}+\\mathrm{e}^{-E_{2} / k T}}{\\mathrm{e}^{-E_{2} / k T}}$\n\nE. $\\frac{\\mathrm{e}^{-E_{1} / k T}+\\mathrm{e}^{-E_{2} / k T}}{\\mathrm{e}^{-E_{1} / k T}}$\n\n$$\n\\left(p+\\frac{a}{V^{2}}\\right)(V-b)=R T\n$$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "Consider 1 mole of a real gas that obeys the van der Waals equation of state shown above. If the gas undergoes an isothermal expansion at temperature $T_{0}$ from volume $V_{1}$ to volume $V_{2}$, which of the following gives the work done by the gas?\n\nA. 0\n\nB. $R T_{0} \\ln \\left(\\frac{V_{2}}{V_{1}}\\right)$\n\nC. $R T_{0} \\ln \\left(\\frac{V_{2}-b}{V_{1}-b}\\right)$\n\nD. $R T_{0} \\ln \\left(\\frac{V_{2}-b}{V_{1}-b}\\right)+a\\left(\\frac{1}{V_{2}}-\\frac{1}{V_{1}}\\right)$\n\nE. $R T_{0}\\left(\\frac{1}{\\left(V_{2}-b\\right)^{2}}-\\frac{1}{\\left(V_{1}-b\\right)^{2}}\\right)+a\\left(\\frac{1}{V_{2}^{3}}-\\frac{1}{V_{1}^{3}}\\right)$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "A $1 \\mathrm{~kg}$ block attached to a spring vibrates with a frequency of $1 \\mathrm{~Hz}$ on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an $8 \\mathrm{~kg}$ block placed on the same table. Which of the following gives the frequency of vibration of the $8 \\mathrm{~kg}$ block?\n\nA. $\\frac{1}{4} \\mathrm{~Hz}$\n\nB. $\\frac{1}{2 \\sqrt{2}} \\mathrm{~Hz}$\n\nC. $\\frac{1}{2} \\mathrm{~Hz}$\n\nD. $1 \\mathrm{~Hz}$\n\nE. $2 \\mathrm{~Hz}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "A uniform disk with a mass of $m$ and a radius of $r$ rolls without slipping along a horizontal surface and ramp, as shown above. The disk has an initial velocity of $v$. What is the maximum height $h$ to which the center of mass of the disk rises?\n\nA. $h=\\frac{v^{2}}{2 g}$\n\nB. $h=\\frac{3 v^{2}}{4 g}$\n\nC. $h=\\frac{v^{2}}{g}$\n\nD. $h=\\frac{3 v^{2}}{2 g}$\n\nE. $h=\\frac{2 v^{2}}{g}$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "A mass, $m$, is attached to a massless spring fixed at one end. The mass is confined to move in a horizontal plane, and its position is given by the polar coordinates $r$ and $\\theta$. Both $r$ and $\\theta$ can vary. If the relaxed length of the spring is $s$ and the force constant is $k$, what is the Lagrangian, $L$, for the system?\n\nA. $L=\\frac{1}{2} m \\dot{r}^{2}+\\frac{1}{2} m r^{2} \\dot{\\theta}^{2}-\\frac{1}{2} k(r \\cos \\theta-s)^{2}$\n\nB. $L=\\frac{1}{2} m \\dot{r}^{2}+\\frac{1}{2} m r^{2} \\dot{\\theta}^{2}-\\frac{1}{2} k(r \\sin \\theta-s)^{2}$\n\nC. $L=\\frac{1}{2} m \\dot{r}^{2}+\\frac{1}{2} m r^{2} \\dot{\\theta}^{2}+\\frac{1}{2} k(r-s)^{2}$\n\nD. $L=\\frac{1}{2} m \\dot{r}^{2}+\\frac{1}{2} m r^{2} \\dot{\\theta}^{2}-\\frac{1}{2} k(r-s)^{2}$\n\nE. $L=-\\frac{1}{2} m \\dot{r}^{2}+\\frac{1}{2} m r^{2} \\dot{\\theta}^{2}+\\frac{1}{2} k(r-s)^{2}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "A mass $m$ attached to the end of a massless rod of length $L$ is free to swing below the plane of support, as shown in the figure above. The Hamiltonian for this system is given by\n\n$$\nH=\\frac{p_{\\theta}^{2}}{2 m L^{2}}+\\frac{p_{\\phi}^{2}}{2 m L^{2} \\sin ^{2} \\theta}-m g L \\cos \\theta\n$$\n\nwhere $\\theta$ and $\\phi$ are defined as shown in the figure. On the basis of Hamilton's equations of motion, the generalized coordinate or momentum that is a constant in time is\n\nA. $\\theta$\n\nB. $\\phi$\n\nC. $\\dot{\\theta}$\n\nD. $p_{\\theta}$\n\nE. $p_{\\phi}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "A rod of length $L$ and mass $M$ is placed along the $x$-axis with one end at the origin, as shown in the figure above. The rod has linear mass density $\\lambda=\\frac{2 M}{L^{2}} x$, where $x$ is the distance from the origin. Which of the following gives the $x$-coordinate of the rod's center of mass?\n\nA. $\\frac{1}{12} L$\n\nB. $\\frac{1}{4} L$\n\nC. $\\frac{1}{3} L$\n\nD. $\\frac{1}{2} L$\n\nE. $\\frac{2}{3} L$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "A particle is in an infinite square well potential with walls at $x=0$ and $x=L$. If the particle is in the state $\\psi(x)=A \\sin \\left(\\frac{3 \\pi x}{L}\\right)$, where $A$ is a constant, what is the probability that the particle is between $x=\\frac{1}{3} L$ and $x=\\frac{2}{3} L$ ?\n\nA. 0\n\nB. $\\frac{1}{3}$\n\nC. $\\frac{1}{\\sqrt{3}}$\n\nD. $\\frac{2}{3}$\n\nE. 1", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "Which of the following are the eigenvalues of the Hermitian matrix $\\left(\\begin{array}{cc}2 & i \\\\ -i & 2\\end{array}\\right)$ ?\n\nA. 1,0\n\nB. 1,3\n\nC. 2,2\n\nD. $i,-i$\n\nE. $1+i, 1-i$\n\n$$\n\\sigma_{x}=\\left(\\begin{array}{ll}\n0 & 1 \\\\\n1 & 0\n\\end{array}\\right), \\quad \\sigma_{y}=\\left(\\begin{array}{cc}\n0 & -i \\\\\ni & 0\n\\end{array}\\right), \\quad \\sigma_{z}=\\left(\\begin{array}{cc}\n1 & 0 \\\\\n0 & -1\n\\end{array}\\right), \\quad I=\\left(\\begin{array}{ll}\n1 & 0 \\\\\n0 & 1\n\\end{array}\\right)\n$$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "Consider the Pauli spin matrices $\\sigma_{x}, \\sigma_{y}$, and $\\sigma_{z}$ and the identity matrix $I$ given above. The commutator $\\left[\\sigma_{x}, \\sigma_{y}\\right] \\equiv \\sigma_{x} \\sigma_{y}-\\sigma_{y} \\sigma_{x}$ is equal to which of the following?\n\nA. $I$\n\nB. $2 i \\sigma_{x}$\n\nC. $2 i \\sigma_{y}$\n\nD. $2 i \\sigma_{z}$\n\nE. 0\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "A spin- $\\frac{1}{2}$ particle is in a state described by the spinor\n\n$$\n\\chi=A\\left(\\begin{array}{c}\n1+i \\\\\n2\n\\end{array}\\right)\n$$\n\nwhere $A$ is a normalization constant. The probability of finding the particle with spin projection $S_{z}=-\\frac{1}{2} \\hbar$ is\n\nA. $\\frac{1}{6}$\n\nB. $\\frac{1}{3}$\n\nC. $\\frac{1}{2}$\n\nD. $\\frac{2}{3}$\n\nE. 1\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "An electron with total energy $E$ in the region $x<0$ is moving in the $+x$-direction. It encounters a step potential at $x=0$. The wave function for $x \\leq 0$ is given by\n\n$$\n\\psi=A \\mathrm{e}^{i k_{1} x}+B \\mathrm{e}^{-i k_{1} x}, \\text { where } k_{1}=\\sqrt{\\frac{2 m E}{\\hbar^{2}}}\n$$\n\nand the wave function for $x>0$ is given by\n\n$$\n\\psi=C \\mathrm{e}^{i k_{2} x}, \\text { where } k_{2}=\\sqrt{\\frac{2 m\\left(E-V_{0}\\right)}{\\hbar^{2}}}\n$$\n\nWhich of the following gives the reflection coefficient for the system?\n\nA. $R=0$\n\nB. $R=1$\n\nC. $R=\\frac{k_{2}}{k_{1}}$\n\nD. $R=\\left(\\frac{k_{1}-k_{2}}{k_{1}+k_{2}}\\right)^{2}$\n\nE. $R=\\frac{4 k_{1} k_{2}}{\\left(k_{1}+k_{2}\\right)^{2}}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "Two thin, concentric, spherical conducting shells are arranged as shown in the figure above. The inner shell has radius $a$, charge $+Q$, and is at zero electric potential. The outer shell has radius $b$ and charge $-Q$. If $r$ is the radial distance from the center of the spheres, what is the electric potential in region I $(a<r<b)$ and in region II $(r>b)$ ?\n\n\\section*{Region I}\n\n\\section*{Region II}\n\nA. $\\frac{Q}{4 \\pi \\varepsilon_{0}} \\frac{1}{r}$\n\nB. $\\frac{Q}{4 \\pi \\varepsilon_{0}}\\left(\\frac{1}{r}-\\frac{1}{a}\\right)$ 0\n\nC. $\\frac{Q}{4 \\pi \\varepsilon_{0}}\\left(\\frac{1}{r}-\\frac{1}{b}\\right)$ $-\\frac{Q}{4 \\pi \\varepsilon_{0}} \\frac{1}{r}$\n\nD. $\\frac{Q}{4 \\pi \\varepsilon_{0}}\\left(\\frac{1}{r}-\\frac{1}{a}\\right)$\n\n$\\frac{Q}{4 \\pi \\varepsilon_{0}}\\left(\\frac{1}{b}-\\frac{1}{a}\\right)$\n\nE. $\\frac{Q}{4 \\pi \\varepsilon_{0}}\\left(\\frac{1}{r}-\\frac{1}{b}\\right)$\n\n$\\frac{Q}{4 \\pi \\varepsilon_{0}}\\left(\\frac{1}{a}-\\frac{1}{b}\\right)$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "In static electromagnetism, let $\\mathbf{E}, \\mathbf{B}, \\mathbf{J}$, and $\\rho$ be the electric field, magnetic field, current density, and charge density, respectively. Which of the following conditions allows the electric field to be written in the form $\\mathbf{E}=-\\nabla \\phi$, where $\\phi$ is the electrostatic potential?\n\nA. $\\nabla \\cdot \\mathbf{J}=0$\n\nB. $\\nabla \\cdot \\mathbf{E}=\\rho / \\epsilon_{0}$\n\nC. $\\nabla \\times \\mathbf{E}=\\mathbf{0}$\n\nD. $\\nabla \\times \\mathbf{B}=\\mu_{0} \\mathbf{J}$\n\nE. $\\nabla \\cdot \\mathbf{B}=0$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "A long, straight, hollow cylindrical wire with an inner radius $R$ and an outer radius $2 R$ carries a uniform current density. Which of the following graphs best represents the magnitude of the magnetic field as a function of the distance from the center of the wire?\n\nA.\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "A parallel-plate capacitor has plate separation $d$. The space between the plates is empty. A battery supplying voltage $V_{0}$ is connected across the capacitor, resulting in electromagnetic energy $U_{0}$ stored in the capacitor. A dielectric, of dielectric constant $\\kappa$, is inserted so that it just fills the space between the plates. If the battery is still connected, what are the electric field $E$ and the energy $U$ stored in the dielectric, in terms of $V_{0}$ and $U_{0}$ ?\n$\\underline{E}$\n$\\underline{U}$\nA. $\\frac{V_{0}}{d}$\n$U_{0}$\nB. $\\frac{V_{0}}{d}$\n$\\kappa U_{0}$\nC. $\\frac{V_{0}}{d}$\n$\\kappa^{2} U_{0}$\nD. $\\frac{V_{0}}{\\kappa d}$\n$U_{0}$\nE. $\\frac{V_{0}}{\\kappa d}$\n$\\kappa U_{0}$\n", "target_scores": {"A": 0, "B": 1, "C": 0, "D": 0, "E": 0}, "has_image": false}
{"input": "An observer $O$ at rest midway between two sources of light at $x=0$ and $x=10 \\mathrm{~m}$ observes the two sources to flash simultaneously. According to a second observer $O^{\\prime}$, moving at a constant speed parallel to the $x$-axis, one source of light flashes $13 \\mathrm{~ns}$ before the other. Which of the following gives the speed of $O^{\\prime}$ relative to $O$ ?\n\nA. $0.13 c$\n\nB. $0.15 c$\n\nC. $0.36 c$\n\nD. $0.53 c$\n\nE. $0.62 c$\n", "target_scores": {"A": 0, "B": 0, "C": 1, "D": 0, "E": 0}, "has_image": false}
{"input": "Let $\\hat{\\mathbf{J}}$ be a quantum mechanical angular momentum operator. The commutator $\\left[\\hat{J}_{x} \\hat{J}_{y}, \\hat{J}_{x}\\right]$ is equivalent to which of the following?\n\nA. 0\n\nB. $i \\hbar \\hat{J}_{z}$\n\nC. $i \\hbar \\hat{J}_{z} \\hat{J}_{x}$\n\nD. $-i \\hbar \\hat{J}_{x} \\hat{J}_{z}$\n\nE. $i \\hbar \\hat{J}_{x} \\hat{J}_{y}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "Which of the following ions CANNOT be used as a dopant in germanium to make an $n$-type semiconductor?\n\nA. As\n\nB. $\\mathrm{P}$\n\nC. $\\mathrm{Sb}$\n\nD. $\\mathrm{B}$\n\nE. $\\mathrm{N}$", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "In the Compton effect, a photon with energy $E$ scatters through a $90^{\\circ}$ angle from a stationary electron of mass $m$. The energy of the scattered photon is\n\nA. $E$\n\nB. $\\frac{E}{2}$\n\nC. $\\frac{E^{2}}{m c^{2}}$\n\nD. $\\frac{E^{2}}{E+m c^{2}}$\n\nE. $\\frac{E \\cdot m c^{2}}{E+m c^{2}}$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "Which of the following is the principal decay mode of the positive muon $\\mu^{+}$?\n\nA. $\\mu^{+} \\rightarrow e^{+}+v_{e}$\n\nB. $\\mu^{+} \\rightarrow p+v_{\\mu}$\n\nC. $\\mu^{+} \\rightarrow n+e^{+}+v_{e}$\n\nD. $\\mu^{+} \\rightarrow e^{+}+v_{e}+\\bar{v}_{\\mu}$\n\nE. $\\mu^{+} \\rightarrow \\pi^{+}+\\bar{v}_{e}+v_{\\mu}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 1, "E": 0}, "has_image": false}
{"input": "A small particle of mass $m$ is at rest on a horizontal circular platform that is free to rotate about a vertical axis through its center. The particle is located at a radius $r$ from the axis, as shown in the figure above. The platform begins to rotate with constant angular acceleration $\\alpha$. Because of friction between the particle and the platform, the particle remains at rest with respect to the platform. When the platform has reached angular speed $\\omega$, the angle $\\theta$ between the static frictional force $\\mathbf{f}_{\\mathrm{s}}$ and the inward radial direction is given by which of the following?\n\nA. $\\theta=\\frac{\\omega^{2} r}{g}$\n\nB. $\\theta=\\frac{\\omega^{2}}{\\alpha}$\n\nC. $\\theta=\\frac{\\alpha}{\\omega^{2}}$\n\nD. $\\theta=\\tan ^{-1}\\left(\\frac{\\omega^{2}}{\\alpha}\\right)$\n\nE. $\\theta=\\tan ^{-1}\\left(\\frac{\\alpha}{\\omega^{2}}\\right)$\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}
{"input": "The partition function $Z$ in statistical mechanics can be written as\n\n$$\nZ=\\sum_{r} \\mathrm{e}^{-E_{r} / k T}\n$$\n\nwhere the index $r$ ranges over all possible microstates of a system and $E_{r}$ is the energy of microstate $r$. For a single quantum mechanical harmonic oscillator with energies\n\n$$\nE_{n}=\\left(n+\\frac{1}{2}\\right) \\hbar \\omega, \\text { where } n=0,1,2, \\ldots,\n$$\n\nthe partition function $Z$ is given by which of the following?\n\nA. $Z=\\mathrm{e}^{-\\frac{1}{2} \\hbar \\omega / k T}$\n\nB. $Z=\\mathrm{e}^{\\frac{1}{2} \\hbar \\omega / k T}$\n\nC. $Z=\\mathrm{e}^{\\frac{1}{2} \\hbar \\omega / k T}-1$\n\nD. $Z=\\mathrm{e}^{\\frac{1}{2} \\hbar \\omega / k T}+1$\n\nE. $Z=\\frac{\\mathrm{e}^{\\frac{1}{2} \\hbar \\omega / k T}}{\\mathrm{e}^{\\hbar \\omega / k T}-1}$\n\n", "target_scores": {"A": 0, "B": 0, "C": 0, "D": 0, "E": 1}, "has_image": false}