shayekh/physics_gre huggingface dataset:
An atom has filled $n=1$ and $n=2$ levels. How many electrons does the atom have?

A. 2

B. 4

C. 6

D. 8

E. 10
Answer scores:
A: 0
B: 0
C: 0
D: 0
E: 1
The root-mean-square speed of molecules of mass $m$ in an ideal gas at temperature $T$ is

A. 0

B. $\sqrt{\frac{2 k T}{m}}$

C. $\sqrt{\frac{3 k T}{m}}$

D. $\sqrt{\frac{8 k T}{\pi m}}$

E. $\frac{k T}{m}$

Answer scores:
A: 0
B: 0
C: 1
D: 0
E: 0
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

A. 2

B. 4

C. 8

D. 16

E. 32


Answer scores:
A: 0
B: 0
C: 0
D: 1
E: 0
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?

I. Area $A=\operatorname{area} B$

II. The star $S$ is at one focus of an elliptically shaped orbit.

III. $T^{2}=C a^{3}$, where $a$ is the semimajor axis of the ellipse and $C$ is a constant.

A. I only

B. II only

C. I and II only

D. II and III only

E. I, II, and III

Answer scores:
A: 0
B: 0
C: 0
D: 0
E: 1
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?

A. $s=v \sqrt{\frac{k}{m}}$

B. $s=v \sqrt{\frac{m}{k}}$

C. $s=v \sqrt{\frac{2 k}{m}}$

D. $s=v \frac{m}{k}$

E. $s=v^{2} \frac{m}{2 k}$
Answer scores:
A: 0
B: 1
C: 0
D: 0
E: 0
A quantum mechanical harmonic oscillator has an angular frequency $\omega$. The Schrödinger equation predicts that the ground state energy of the oscillator will be

A. $-\frac{1}{2} \hbar \omega$

B. 0

C. $\frac{1}{2} \hbar \omega$

D. $\hbar \omega$

E. $\frac{3}{2} \hbar \omega$

Answer scores:
A: 0
B: 0
C: 1
D: 0
E: 0
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.)

A. $n \hbar$

B. $n r_{n} \hbar$

C. $\frac{n \hbar}{r_{n}}$

D. $n^{2} r_{n} \hbar$

E. $\frac{n^{2} \hbar}{r_{n}}$


Answer scores:
A: 0
B: 0
C: 1
D: 0
E: 0
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 $x$ ?

A. $y=6 \sqrt{x}$

B. $y=\frac{1}{2} x+6$

C. $y=6 x+0.5$

D. $y=\frac{1}{6} x^{2}$

E. $y=6 x^{2}$

Answer scores:
A: 1
B: 0
C: 0
D: 0
E: 0
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?

A. $\frac{1}{2} \mathrm{~kg}$

B. $\frac{2}{\sqrt{5}} \mathrm{~kg}$

C. $\frac{2}{\sqrt{3}} \mathrm{~kg}$

D. $2 \mathrm{~kg}$

E. $\sqrt{5} \mathrm{~kg}$
Answer scores:
A: 0
B: 1
C: 0
D: 0
E: 0
If the five lenses shown below are made of the same material, which lens has the shortest positive focal length?

A.


Answer scores:
A: 0
B: 0
C: 0
D: 0
E: 1
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?

A. $100 \%$

B. $75 \%$

C. $50 \%$

D. $25 \%$

E. $0 \%$

Answer scores:
A: 0
B: 0
C: 0
D: 1
E: 0
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?

A. $\frac{1}{2 \pi \varepsilon_{0}} \frac{\lambda}{r}$

B. $\frac{1}{2 \pi \varepsilon_{0}} \frac{r}{\lambda}$

C. $\frac{1}{2 \pi \varepsilon_{0}} \frac{\lambda}{r^{2}}$

D. $\frac{1}{4 \pi \varepsilon_{0}} \frac{\lambda^{2}}{r^{2}}$

E. $\frac{1}{4 \pi \varepsilon_{0}} \lambda \ln r$


Answer scores:
A: 1
B: 0
C: 0
D: 0
E: 0
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?

A. No current flows between $a$ and $b$ as the magnet passes through the loop.

B. Current flows from $a$ to $b$ as the magnet passes through the loop.

C. Current flows from $b$ to $a$ as the magnet passes through the loop.

D. Current flows from $a$ to $b$ as the magnet enters the loop and from $b$ to $a$ as the magnet leaves the loop.

E. Current flows from $b$ to $a$ as the magnet enters the loop and from $a$ to $b$ as the magnet leaves the loop.

Answer scores:
A: 0
B: 0
C: 0
D: 0
E: 1
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?

A. $10 \mu \mathrm{m}$

B. $100 \mu \mathrm{m}$

C. $10 \mathrm{~mm}$

D. $100 \mathrm{~mm}$

E. $10 \mathrm{~m}$

Answer scores:
A: 1
B: 0
C: 0
D: 0
E: 0
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

A. one-quarter as distant as they are today

B. one-half as distant as they are today

C. separated by about the same distances as they are today

D. two times as distant as they are today

E. four times as distant as they are today

Answer scores:
A: 1
B: 0
C: 0
D: 0
E: 0
For an adiabatic process involving an ideal gas having volume $V$ and temperature $T$, which of the following is constant? $\left(\gamma=C_{P} / C_{V}\right)$

A. $T V$

B. $T V^{\gamma}$

C. $T V^{\gamma-1}$

D. $T^{\gamma} V$

E. $T^{\gamma} V^{-1}$
Answer scores:
A: 0
B: 0
C: 1
D: 0
E: 0
An electron has total energy equal to four times its rest energy. The momentum of the electron is

A. $m_{e} c$

B. $\sqrt{2} m_{e} c$

C. $\sqrt{15} m_{e} c$

D. $4 m_{e} c$

E. $2 \sqrt{15} m_{e} c$

Answer scores:
A: 0
B: 0
C: 1
D: 0
E: 0
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?

A. $0.4 c$

B. $0.5 c$

C. $0.6 c$

D. $0.7 c$

E. $0.8 c$

Answer scores:
A: 0
B: 1
C: 0
D: 0
E: 0
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?

A. $1.6 \mathrm{~ns}$

B. $2.5 \mathrm{~ns}$

C. $4.2 \mathrm{~ns}$

D. $6.9 \mathrm{~ns}$

E. $8.3 \mathrm{~ns}$

Answer scores:
A: 0
B: 1
C: 0
D: 0
E: 0
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 $\{1,2, \ldots, n\}$. )

A. $\psi_{i}^{*}(x) \psi_{j}(x)=0$

B. $\psi_{i}^{*}(x) \psi_{j}(x)=1$

C. $\int_{-\infty}^{\infty} \psi_{i}^{*}(x) \psi_{j}(x) d x=0$

D. $\int_{-\infty}^{\infty} \psi_{i}^{*}(x) \psi_{j}(x) d x=1$

E. $\int_{-\infty}^{\infty} \psi_{i}^{*}(x) \psi_{j}(x) d x=\delta_{i j}$

Answer scores:
A: 0
B: 0
C: 0
D: 0
E: 1
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?

A. 0

B. $\frac{a_{0}}{2}$

C. $\frac{a_{0}}{\sqrt{2}}$

D. $a_{0}$

E. $2 a_{0}$
Answer scores:
A: 0
B: 0
C: 0
D: 1
E: 0
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

A. $100 \mathrm{~Hz}$

B. $100 \mathrm{kHz}$

C. $100 \mathrm{MHz}$

D. $100 \mathrm{GHz}$

E. $100 \mathrm{THz}$

Answer scores:
A: 0
B: 0
C: 1
D: 0
E: 0
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

A. $k$

B. $2 k$

C. $4 k$

D. $8 k$

E. $16 k$

Answer scores:
A: 0
B: 0
C: 0
D: 1
E: 0
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

A. $\frac{\sqrt{3}}{4} v$

B. $\frac{v}{2}$

C. $\frac{\sqrt{3}}{2} v$

D. $\frac{\sqrt{5}}{2} v$

E. $v+\frac{v}{2} \cos \theta$

Answer scores:
A: 0
B: 0
C: 1
D: 0
E: 0
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.)

A. $q_{i}=\frac{\partial H}{\partial p_{i}}, \quad p_{i}=-\frac{\partial H}{\partial q_{i}}$

B. $q_{i}=\frac{\partial H}{\partial \dot{q}_{i}}, \quad p_{i}=\frac{\partial H}{\partial \dot{p}_{i}}$

C. $\dot{q}_{i}=\frac{\partial H}{\partial q_{i}}, \quad \dot{p}_{i}=-\frac{\partial H}{\partial p_{i}}$

D. $\dot{q}_{i}=\frac{\partial H}{\partial p_{i}}, \quad \dot{p}_{i}=-\frac{\partial H}{\partial q_{i}}$

E. $\frac{d}{d t}\left(\frac{\partial H}{\partial p_{i}}\right)-\frac{\partial H}{\partial q_{i}}=0$

\begin{tabular}{|l|}
\hline Oil \\
\hline Water \\
\hline
\end{tabular}

Answer scores:
A: 0
B: 0
C: 0
D: 1
E: 0
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?

A. $200 \mathrm{~kg} / \mathrm{m}^{3}$

B. $850 \mathrm{~kg} / \mathrm{m}^{3}$

C. $950 \mathrm{~kg} / \mathrm{m}^{3}$

D. $1,050 \mathrm{~kg} / \mathrm{m}^{3}$

E. $1,800 \mathrm{~kg} / \mathrm{m}^{3}$
Answer scores:
A: 0
B: 0
C: 1
D: 0
E: 0
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

A. $P_{0}-\frac{15}{2} \rho v_{0}^{2}$

B. $P_{0}-\frac{3}{2} \rho v_{0}^{2}$

C. $\frac{P_{0}}{4}$

D. $P_{0}+\frac{3}{2} \rho v_{0}^{2}$

E. $P_{0}+\frac{15}{2} \rho v_{0}^{2}$

Answer scores:
A: 1
B: 0
C: 0
D: 0
E: 0
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

A. 0

B. $T_{2}-T_{1}$

C. $m c T_{2}$

D. $m c\left(T_{2}-T_{1}\right)$

E. $m c \ln \left(\frac{T_{2}}{T_{1}}\right)$

Answer scores:
A: 0
B: 0
C: 0
D: 0
E: 1
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?

A. $\frac{3}{5} Q$

B. $Q$

C. $\frac{5}{3} Q$

D. $2 Q$

E. $\frac{10}{3} Q$
Answer scores:
A: 0
B: 0
C: 1
D: 0
E: 0
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

A. $500 \mathrm{~J}$

B. $1,000 \mathrm{~J}$

C. $1,100 \mathrm{~J}$

D. $2,000 \mathrm{~J}$

E. $2,200 \mathrm{~J}$


Answer scores:
A: 0
B: 1
C: 0
D: 0
E: 0
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.)

A.


Answer scores:
A: 1
B: 0
C: 0
D: 0
E: 0
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?
Magnitude
Direction
A. $\frac{1}{4 \pi \epsilon_{0}} \frac{2 q}{r^{2}}$
$+y$
B. $\frac{1}{4 \pi \epsilon_{0}} \frac{2 q}{r^{2}}$
$+x$
C. $\frac{1}{4 \pi \epsilon_{0}} \frac{2 q}{r^{2}}$
$-x$
D. $\frac{1}{4 \pi \epsilon_{0}} \frac{q \ell}{r^{3}}$
$+x$
E. $\frac{1}{4 \pi \epsilon_{0}} \frac{q \ell}{r^{3}}$

Answer scores:
A: 0
B: 0
C: 0
D: 0
E: 1
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 $P$ ?

A. $\frac{\mu_{0} I}{2 \pi a}(\hat{\mathbf{x}}+\hat{\mathbf{y}})$

B. $-\frac{\mu_{0} I}{2 \pi a}(\hat{\mathbf{x}}+\hat{\mathbf{y}})$

C. $\frac{\mu_{0} I}{\pi a} \hat{\mathbf{z}}$

D. $-\frac{\mu_{0} I}{\pi a} \hat{\mathbf{z}}$

E. 0

Answer scores:
A: 0
B: 0
C: 0
D: 0
E: 1
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

A. $530 \mathrm{~m}$

B. $660 \mathrm{~m}$

C. $880 \mathrm{~m}$

D. $1,100 \mathrm{~m}$

E. $1,500 \mathrm{~m}$

Answer scores:
A: 0
B: 0
C: 1
D: 0
E: 0
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

A. $\frac{\left(M^{2}-m^{2}\right) c}{4 M}$

B. $\frac{\left(M^{2}-m^{2}\right) c}{2 M}$

C. $\frac{\left(M^{2}-m^{2}\right) c}{M}$

D. $\frac{2\left(M^{2}-m^{2}\right) c}{M}$

E. $\frac{4\left(M^{2}-m^{2}\right) c}{M}$


Answer scores:
A: 0
B: 1
C: 0
D: 0
E: 0
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 $\phi$.)

A. $\frac{h}{\phi}$

B. $\frac{h}{e}$

C. $\frac{e}{h}$

D. $\frac{e}{\phi}$

E. $\frac{\phi}{e}$


Answer scores:
A: 0
B: 1
C: 0
D: 0
E: 0
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

A. $30^{\circ}$

B. $45^{\circ}$

C. $60^{\circ}$

D. $90^{\circ}$

E. $120^{\circ}$

Answer scores:
A: 0
B: 0
C: 0
D: 0
E: 1
In the diamond structure of elemental carbon, the nearest neighbors of each $\mathrm{C}$ atom lie at the corners of a

A. square

B. hexagon

C. cube

D. tetrahedron

E. octahedron
Answer scores:
A: 0
B: 0
C: 0
D: 1
E: 0
According to the BCS theory, the attraction between Cooper pairs in a superconductor is due to

A. the weak nuclear force

B. the strong nuclear force

C. vacuum polarization

D. interactions with the ionic lattice

E. the Casimir effect

Answer scores:
A: 0
B: 0
C: 0
D: 1
E: 0
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 $330 \mathrm{~m} / \mathrm{s}$.)

A. $1,000 \mathrm{~Hz}$

B. $1,030 \mathrm{~Hz}$

C. $1,200 \mathrm{~Hz}$

D. $1,400 \mathrm{~Hz}$

E. $1,440 \mathrm{~Hz}$

Answer scores:
A: 0
B: 0
C: 1
D: 0
E: 0
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?

A. $500 \mathrm{~Hz}$

B. $1,750 \mathrm{~Hz}$

C. $2,750 \mathrm{~Hz}$

D. $3,500 \mathrm{~Hz}$

E. $5,000 \mathrm{~Hz}$

Answer scores:
A: 0
B: 0
C: 0
D: 1
E: 0
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?

A. $44 \mathrm{~Hz}$

B. $196 \mathrm{~Hz}$

C. $262 \mathrm{~Hz}$

D. $393 \mathrm{~Hz}$

E. $524 \mathrm{~Hz}$

Inputs


Answer scores:
A: 0
B: 0
C: 0
D: 1
E: 0
For the logic circuit shown above, which of the following Boolean statements gives the output $E$ in terms of inputs $A, B, C$, and $D$ ?

A. $E=\overline{A+B}+\overline{C \cdot D}$

B. $E=\overline{A+B} \cdot \overline{C \cdot D}$

C. $E=\overline{\bar{A}+\bar{B}} \cdot \overline{C \cdot D}$

D. $E=\overline{A \cdot B} \cdot \overline{C \cdot D}$

E. $E=\overline{\bar{A} \cdot \bar{B}} \cdot \overline{C \cdot D}$

Answer scores:
A: 0
B: 0
C: 1
D: 0
E: 0
Which of the following lasers utilizes transitions that involve the energy levels of free atoms?

A. Diode laser

B. Dye laser

C. Free-electron laser

D. Gas laser

E. Solid-state laser
Answer scores:
A: 0
B: 0
C: 0
D: 1
E: 0
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.)

A. $\frac{m Z e^{2}}{n}$

B. $\frac{m Z e^{2}}{n^{2}}$

C. $\frac{m Z^{2} e^{4}}{n^{2}}$

D. $\frac{m^{2} Z^{2} e^{2}}{n^{2}}$

E. $\frac{m^{2} Z^{2} e^{4}}{n^{2}}$

Answer scores:
A: 0
B: 0
C: 1
D: 0
E: 0
True statements about the absorption and emission of energy by an atom include which of the following?

I. An atom can only absorb photons of light that have certain specific energies.

II. An atom can emit photons of light of any energy.

III. 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.

A. I only

B. III only

C. I and II only

D. I and III only

E. I, II, and III

Answer scores:
A: 0
B: 0
C: 0
D: 1
E: 0
$X$ 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 $d ?\left(\sin 14.5^{\circ} \approx 1 / 4\right)$

A. $0.125 \mathrm{~nm}$

B. $0.250 \mathrm{~nm}$

C. $0.500 \mathrm{~nm}$

D. $0.625 \mathrm{~nm}$

E. $0.750 \mathrm{~nm}$

Answer scores:
A: 0
B: 0
C: 1
D: 0
E: 0
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

A. 1

B. $\sqrt{3}$

C. 2

D. 3

E. 9

Answer scores:
A: 0
B: 0
C: 0
D: 1
E: 0
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?

A. The planets would move directly toward the Sun.

B. The planets would move in spiral orbits.

C. The planets would oscillate about their former elliptical orbits.

D. The orbits would precess much more rapidly.

E. The orbits would remain unchanged.
Answer scores:
A: 0
B: 0
C: 0
D: 0
E: 1
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: $\frac{580}{434} \approx \frac{4}{3}$ )

A. $0.28 c$

B. $0.53 c$

C. $0.56 c$

D. $0.75 c$

E. $0.86 c$

Answer scores:
A: 1
B: 0
C: 0
D: 0
E: 0
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?

A. $\frac{50}{23} \mathrm{~h}$

B. $\frac{50}{\sqrt{409}} \mathrm{~h}$

C. $\frac{50}{20} \mathrm{~h}$

D. $\frac{50}{\sqrt{391}} \mathrm{~h}$

E. $\frac{50}{17} \mathrm{~h}$


Answer scores:
A: 0
B: 0
C: 0
D: 1
E: 0
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.)

\section*{Figure 1}

A. $F_{12}=\frac{F}{3}$

B. $F_{12}=\frac{F}{3}$

C. $F_{12}=\frac{2 F}{3}$

D. $F_{12}=\frac{2 F}{3}$

E. $F_{12}=F$

\section*{Figure 2}

$$
F_{12}=\frac{F}{3}
$$

$F_{12}=\frac{2 F}{3}$

$F_{12}=\frac{F}{3}$

$F_{12}=\frac{2 F}{3}$

$F_{12}=F$


Answer scores:
A: 0
B: 1
C: 0
D: 0
E: 0
In the figure above, block $A$ has mass

$m_{A}=25 \mathrm{~kg}$ and block $B$ has mass $m_{B}=10 \mathrm{~kg}$.

Both 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

A. $20 \mathrm{~N}$

B. $50 \mathrm{~N}$

C. $78 \mathrm{~N}$

D. $196 \mathrm{~N}$

E. $274 \mathrm{~N}$

Answer scores:
A: 1
B: 0
C: 0
D: 0
E: 0
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

A. $T=2 \pi \sqrt{\frac{l}{g}}$

B. $T=2 \pi \sqrt{\frac{l}{g-a}}$

C. $T=2 \pi \sqrt{\frac{l}{g+a}}$

D. $T=2 \pi \sqrt{\frac{l}{g} \frac{a}{(g+a)}}$

E. $T=2 \pi \sqrt{\frac{l}{g} \frac{(g+a)}{a}}$


Answer scores:
A: 0
B: 0
C: 1
D: 0
E: 0
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

A. $\mathbf{B}=\frac{3 \mu_{0} I}{2 \pi x} \hat{\mathbf{x}}$

B. $\mathbf{B}=\frac{3 \mu_{0} I}{2 \pi x} \hat{\mathbf{y}}$

C. $\mathbf{B}=\frac{\mu_{0} I}{2 \pi x}(1+2 \sqrt{2}) \hat{\mathbf{y}}$

D. $\mathbf{B}=\frac{\mu_{0} I}{2 \pi x} \hat{\mathbf{x}}$

E. $\mathbf{B}=\frac{\mu_{0} I}{2 \pi x} \hat{\mathbf{y}}$


Answer scores:
A: 0
B: 0
C: 1
D: 0
E: 0
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?

A. $2 d$

B. $\sqrt{2} d$

C. $d$

D. $\frac{1}{\sqrt{2}} d$

E. $\frac{1}{2} d$


Answer scores:
A: 0
B: 0
C: 0
D: 0
E: 1