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AP Physics 2 Full-length practice exam 1

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Full-length practice exam 1

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Question 1

An ideal gas is held at constant volume while heat $Q$ is added to it. Which expression correctly gives the change in internal energy $Δ U$ ?

Δ U = Q - W

, where

W = P Δ V > 0

Δ U = Q

Δ U = - Q

Δ U = 0

, because temperature does not change at constant volume.

Question 2

Which of the following processes is impossible according to the second law of thermodynamics?

A.A heat engine converts 40% of absorbed heat into work and rejects the rest.B.Heat flows from a hot object to a cold object when they are in thermal contact.C.A refrigerator removes heat from a cold interior and expels heat to a warm room, using electrical work.D.A cyclic heat engine converts all absorbed heat into work with no heat rejected to a cold reservoir.

Question 3

One mole of an ideal monatomic gas undergoes an isobaric expansion from volume $V_{1}$ to $2 V_{1}$ at pressure $P$ . Which expression correctly gives the heat $Q$ added to the gas? (Use $R$ for the ideal gas constant.)

Q = P V_{1}

Q = \frac{3}{2} P V_{1}

Q = \frac{5}{2} P V_{1}

Q = 2 P V_{1}

Question 4

Two identical samples of an ideal gas start at the same state $(P_{0}, V_{0}, T_{0})$ . Sample A undergoes an adiabatic expansion to volume $2 V_{0}$ . Sample B undergoes an isothermal expansion to volume $2 V_{0}$ . Which sample ends at a higher pressure, and why?

A.Sample A, because adiabatic processes conserve energy better.B.Sample B, because isothermal expansion keeps temperature constant while adiabatic expansion causes cooling.C.Both samples end at the same pressure, because they expand to the same volume.D.Sample A, because adiabatic expansion curves are steeper, reaching higher pressures.

Question 5

An object is placed $15 cm$ to the left of a converging lens with $f_{1} = 10 cm$ . A second converging lens with $f_{2} = 20 cm$ is placed $40 cm$ to the right of the first lens. Where is the final image formed relative to the second lens?

20 cm

to the right of lens 2 (real image)B.

20 cm

to the left of lens 2 (virtual image)C.

13.3 cm

to the right of lens 2 (real image)D.No image is formed — the object is at

f_{2}

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Question 6

A thin film of soap ( $n = 1.35$ ) in air has a thickness $t = 350 nm$ . For what wavelength of visible light (in air) does the film appear brightest (constructive interference in reflection)?

λ = 945 nm

(infrared — not visible)B.

λ = 630 nm

(orange-red)C.

λ = 472.5 nm

(blue-violet)D.

λ = 315 nm

(ultraviolet — not visible)

Question 7

The half-life of a radioactive isotope is $T_{1/2} = 5 days$ . Starting with $N_{0} = 1600$ atoms, how many remain after $20 days$ ?

N = 400

atomsB.

N = 200

atomsC.

N = 100

atomsD.

N = 0

atoms

Question 8

In single-slit diffraction, the first minimum occurs at angle $θ$ given by $a sin θ = λ$ , where $a$ is the slit width. If the slit width is doubled while keeping the wavelength constant, the central diffraction maximum becomes:

A.Twice as wide and half as brightB.Half as wide and more brightC.The same width but twice as brightD.Half as wide and half as bright

Question 9

Point P is located midway between two point charges: $+ 3 Q$ at $x = - d$ and $- Q$ at $x = + d$ . What is the direction of the net electric field at point P ( $x = 0$ )?

A.The field points in the

+ x

direction.B.The field points in the

- x

direction.C.The net field is zero because positive and negative charges cancel.D.The field points in the

+ y

direction.

Question 10

A $P V$ diagram shows a gas undergoing a rectangular cycle (two isobaric and two isochoric processes). In which segment does the gas do the most positive work?

A.The isochoric (constant volume) expansion at high pressure.B.The isobaric compression at low pressure.C.The isobaric expansion at high pressure.D.The isochoric compression at low volume.

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Question 11

A $60 W$ lightbulb is designed to operate at $120 V$ . What is its operating resistance?

R = 0.5 Ω

R = 240 Ω

R = 2 Ω

R = 7200 Ω

Question 12

Two capacitors, $C_{1} = 4 μ F$ and $C_{2} = 12 μ F$ , are connected in series across a $24 V$ battery. What is the charge on $C_{1}$ ?

Q_{1} = 96 μ C

Q_{1} = 288 μ C

Q_{1} = 72 μ C

Q_{1} = 18 μ C

Question 13

A square loop of side $s = 0.2 m$ and resistance $R = 4 Ω$ is in a magnetic field that is increasing at $d B / d t = 50 T/s$ perpendicular to the loop. What is the power dissipated in the loop?

P = 0.25 W

P = 1.0 W

P = 16 W

P = 0.5 W

Question 14

A charge $q = + 2 μ C$ is moved from point A to point B in an electric field. The potential at A is $V_{A} = 100 V$ and at B is $V_{B} = 40 V$ . What is the work done by the electric field on the charge?

W = + 1.2 \times 1 0^{- 4} J

W = - 1.2 \times 1 0^{- 4} J

W = + 2.8 \times 1 0^{- 4} J

W = + 8.0 \times 1 0^{- 5} J

Question 15

An RC circuit has a capacitor $C = 200 μ F$ in series with a resistor $R = 5 k Ω$ and a $12 V$ battery. The capacitor is initially uncharged. Approximately how long after the switch is closed does the voltage across the capacitor reach $7.6 V$ ? (Use $e \approx 2.718$ , so $1 - e^{- 1} \approx 0.632$ .)

t \approx 0.5 s

t \approx 1.0 s

t \approx 2.0 s

t \approx 0.1 s

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Question 16

A fully charged capacitor ( $C = 100 μ F$ , $V_{0} = 10 V$ ) is connected in series with a resistor $R = 2 k Ω$ with no battery. After the switch is closed, what is the current through the resistor at $t = 0$ (immediately after closing)?

I_{0} = 0

I_{0} = 5 mA

I_{0} = 50 mA

I_{0} = 1 A

Question 17

In the Bohr model of hydrogen, an electron transitions from energy level $n = 3$ to $n = 1$ . This transition results in:

A.The absorption of a photon with energy equal to

E_{3} - E_{1}

B.The emission of a photon with energy equal to

E_{3} - E_{1}

C.The emission of a photon with energy equal to

E_{1} - E_{3}

D.No photon is emitted; the electron just loses energy.

Question 18

A positive test charge $+ q$ is placed in an electric field $E$ . The electric force on the test charge is:

F = E / q

F = q E

, directed opposite to

E

since the charge is positive.C.

F = q E

, directed in the same direction as

E

.D.

F = q^{2} E

Question 19

Total internal reflection can occur when light travels from:

A.Air into glass, at any angle of incidenceB.Glass into air, at angles exceeding the critical angleC.Glass into air, at angles smaller than the critical angleD.Air into water, when the beam is nearly parallel to the surface

Question 20

A long straight wire carries current $I$ to the right. A proton (positive charge) is located directly above the wire and is moving to the right (same direction as $I$ ). What is the direction of the magnetic force on the proton?

A.Upward, away from the wireB.Downward, toward the wireC.To the left, opposing the proton's motionD.Out of the page

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Question 21

An ideal gas undergoes the following four-step cycle: (1) isobaric expansion at $P_{H}$ , (2) isochoric pressure drop to $P_{L}$ , (3) isobaric compression at $P_{L}$ , (4) isochoric pressure rise back to $P_{H}$ . If the volume changes from $V_{1}$ to $V_{2} > V_{1}$ , what is the net work done by the gas per cycle?

W_{net} = P_{H} V_{2} - P_{L} V_{1}

W_{net} = (P_{H} - P_{L}) (V_{1} + V_{2})

W_{net} = (P_{H} - P_{L}) (V_{2} - V_{1})

W_{net} = P_{H} (V_{2} - V_{1}) - P_{L} (V_{2} - V_{1}) /2

Question 22

Three point charges are placed along a line: $+ Q$ at $x = 0$ , $- Q$ at $x = d$ , and $+ Q$ at $x = 2 d$ . At the point $x = d$ (the location of the $- Q$ charge), the net electric field due to the other two charges points in which direction?

A.In the

+ x

directionB.In the

- x

directionC.The net electric field at

x = d

from the two

+ Q

charges is zero.D.Perpendicular to the line (in the

y

-direction)

Question 23

A rectangular conducting loop is pulled out of a uniform magnetic field $B$ pointing into the page at constant velocity $v$ . The loop has width $L$ (the side perpendicular to $v$ ). Which expression gives the magnitude of the induced EMF while the loop is being pulled out?

E = B L^{2} v

E = B Lv

E = B v / L

E = B^{2} Lv

Question 24

A dielectric material with dielectric constant $κ = 3$ is inserted between the plates of a parallel-plate capacitor connected to a battery (constant voltage). How does the energy stored in the capacitor change?

A.The stored energy decreases by a factor of 3.B.The stored energy increases by a factor of 3.C.The stored energy is unchanged because the voltage is constant.D.The stored energy increases by a factor of 9.

Question 25

In nuclear physics, a nucleus with mass number $A = 235$ and atomic number $Z = 92$ (uranium-235) undergoes alpha decay. What are the mass number and atomic number of the daughter nucleus?

A = 231

Z = 90

A = 233

Z = 90

A = 231

Z = 91

A = 235

Z = 90

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Question 26

A convex (diverging) mirror always produces what type of image for a real object?

A.Real, inverted, diminishedB.Real, upright, magnifiedC.Virtual, inverted, diminishedD.Virtual, upright, diminished

Question 27

In the Compton effect, an X-ray photon of wavelength $λ_{0}$ scatters off a free electron and the scattered photon has a longer wavelength $λ^{'}$ . The Compton shift $Δ λ = λ^{'} - λ_{0}$ depends on:

A.The initial wavelength

λ_{0}

of the photon onlyB.The scattering angle

θ

only (and fundamental constants)C.Both the initial wavelength and the scattering angleD.The mass of the photon and the electron mass

Question 28

The average kinetic energy of molecules in an ideal monatomic gas at temperature $T$ (in kelvin) is given by:

\overset{ˉ}{K} = k T

\overset{ˉ}{K} = \frac{1}{2} k T

\overset{ˉ}{K} = \frac{3}{2} k T

\overset{ˉ}{K} = \frac{3}{2} n R T

Question 29

A proton moves in a circle of radius $r$ when it enters a region with a uniform magnetic field $B$ perpendicular to its velocity. Which of the following expressions gives the speed of the proton? ( $m_{p}$ = proton mass, $e$ = proton charge)

v = \frac{e B}{m _{p} r}

v = \frac{e B r}{m _{p}}

v = \frac{m _{p} r}{e B}

v = e B r m_{p}

Question 30

A particle is accelerated through a potential difference of $V = 50 kV$ . Using the de Broglie relation $λ = h / p$ and energy conservation (non-relativistic), what is the de Broglie wavelength of a proton accelerated through this potential? ( $m_{p} = 1.67 \times 1 0^{- 27} kg$ , $e = 1.6 \times 1 0^{- 19} C$ , $h = 6.63 \times 1 0^{- 34} J \cdot s$ )

λ \approx 1.28 \times 1 0^{- 13} m

λ \approx 5.5 \times 1 0^{- 12} m

λ \approx 1.28 \times 1 0^{- 10} m

λ \approx 6.63 \times 1 0^{- 34} m

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Question 31

A resistor has a current of $I = 3 A$ flowing through it and a voltage of $V = 12 V$ across it. What is its resistance?

R = 0.25 Ω

R = 4 Ω

R = 36 Ω

R = 9 Ω

Question 32

Light travels from glass ( $n_{g} = 1.5$ ) into water ( $n_{w} = 1.33$ ) at an angle of incidence of $60°$ . What is the angle of refraction in water? ( $sin 60° \approx 0.866$ )

θ_{2} \approx 40.6°

(ray bends toward the normal)B.Total internal reflection occurs; no transmitted ray.C.

θ_{2} \approx 77.8°

(ray bends away from the normal)D.

θ_{2} = 60°

(no bending at the glass-water interface)

Question 33

A circuit has a $9 V$ battery with internal resistance $r = 1 Ω$ connected to an external resistance $R = 8 Ω$ . What is the terminal voltage of the battery?

V_{terminal} = 9 V

V_{terminal} = 8 V

V_{terminal} = 1 V

V_{terminal} = 9.1 V

Question 34

In the photoelectric effect, which property of light determines the maximum kinetic energy of the ejected electrons?

A.The intensity (brightness) of the lightB.The frequency (or wavelength) of the lightC.The angle of incidence of the light on the metalD.The total duration of illumination

Question 35

A proton moves with velocity $v$ in a magnetic field $B$ . The magnetic force on the proton is given by:

F = q v \cdot B

(dot product)B.

F = q v \times B

F = q B \times v

F = q v B

(parallel to

v

)

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Question 36

Snell's law describes refraction at the interface between two media. If a ray travels from medium 1 (index $n_{1}$ ) into medium 2 (index $n_{2} > n_{1}$ ), what happens to the angle of refraction $θ_{2}$ compared to the angle of incidence $θ_{1}$ ?

θ_{2} > θ_{1}

(ray bends away from the normal)B.

θ_{2} < θ_{1}

(ray bends toward the normal)C.

θ_{2} = θ_{1}

(no bending occurs)D.

θ_{2} = 90°

(total internal reflection occurs)

Question 37

A heat engine absorbs $Q_{H} = 800 J$ from a hot reservoir and does $W = 200 J$ of work per cycle. What is the change in entropy of the cold reservoir per cycle if it is at $T_{C} = 400 K$ ?

Δ S_{C} = 0.5 J/K

Δ S_{C} = 1.5 J/K

Δ S_{C} = 2.0 J/K

Δ S_{C} = - 1.5 J/K

Question 38

In a circuit, two batteries are connected in the same loop: Battery 1 has EMF $E_{1} = 12 V$ with internal resistance $r_{1} = 1 Ω$ , and Battery 2 has EMF $E_{2} = 6 V$ with internal resistance $r_{2} = 2 Ω$ . They are connected with opposing polarity (positive terminals facing each other). An external resistance $R = 3 Ω$ completes the loop. What is the current in the loop?

I = 3 A

I = 1 A

I = 2 A

I = 0 A

Question 39

According to the Heisenberg uncertainty principle, the minimum uncertainty in the momentum of an electron confined to a region of length $Δ x = 1.0 \times 1 0^{- 10} m$ (atomic scale) is approximately: ( $h = 6.63 \times 1 0^{- 34} J \cdot s$ )

Δ p \approx 6.63 \times 1 0^{- 24} kg \cdot m/s

Δ p \approx 5.3 \times 1 0^{- 25} kg \cdot m/s

Δ p \approx 1.0 \times 1 0^{- 10} kg \cdot m/s

Δ p \approx 6.63 \times 1 0^{- 44} kg \cdot m/s

Question 40

A gas undergoes an isothermal process. Which of the following is true about the change in internal energy $Δ U$ of an ideal gas during this process?

Δ U > 0

because work is done on the gas.B.

Δ U < 0

because the gas must release heat to maintain constant temperature.C.

Δ U = 0

because internal energy of an ideal gas depends only on temperature.D.

Δ U = Q

because no work is done during an isothermal process.

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Question 41

Two long parallel wires carry equal currents $I$ in opposite directions and are separated by distance $d$ . What is the nature of the magnetic force between them?

A.Attractive, because opposite currents create fields that reinforce between the wires.B.Repulsive, because the magnetic fields between the wires push outward.C.Attractive, same as for parallel currents in the same direction.D.There is no magnetic force because the fields cancel between the wires.

Question 42

Two point charges $+ Q$ and $- Q$ are separated by distance $r$ . According to Coulomb's law, the magnitude of the electric force between them is:

F = \frac{k Q ^{2}}{r}

F = \frac{k Q ^{2}}{r ^{2}}

F = \frac{k Q}{r ^{2}}

F = \frac{2 k Q ^{2}}{r ^{2}}

Question 43

An electron enters a region with both a uniform electric field $E = 1000 V/m$ pointing upward and a uniform magnetic field $B = 0.02 T$ pointing out of the page. The electron moves horizontally to the right without deflection. What must be the speed of the electron?

v = 5 \times 1 0^{4} m/s

v = 2 \times 1 0^{- 5} m/s

v = 5 \times 1 0^{4} m/s

in a specific direction onlyD.

v = 2 \times 1 0^{7} m/s

Question 44

An object is placed $30 cm$ in front of a concave mirror with focal length $f = 10 cm$ . Using the mirror equation $\frac{1}{f} = \frac{1}{d _{o}} + \frac{1}{d _{i}}$ , what is the image distance $d_{i}$ ?

d_{i} = - 15 cm

d_{i} = 15 cm

d_{i} = 20 cm

d_{i} = 40 cm

Question 45

Equipotential surfaces around a positive point charge are:

A.Parallel planes perpendicular to the radial electric field lines.B.Concentric spheres centered on the charge.C.Lines radiating outward from the charge.D.Ellipsoidal surfaces elongated along the direction of the field.

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Question 46

A nuclear reaction fuses two deuterium nuclei to produce helium-3 and a neutron:
$_{1}^{2} H +_{1}^{2} H \to_{2}^{3} He +_{0}^{1} n$
Given that the mass defect is $Δ m = 3.3 \times 1 0^{- 30} kg$ , how much energy is released? ( $c = 3 \times 1 0^{8} m/s$ )

E \approx 2.97 \times 1 0^{- 13} J

E \approx 9.9 \times 1 0^{- 22} J

E \approx 3.0 \times 1 0^{- 13} J

E \approx 9.9 \times 1 0^{- 13} J

Question 47

A converging (convex) lens with focal length $f = 20 cm$ has an object placed $10 cm$ from it (inside the focal length). What type of image does the lens produce?

A.Real, inverted, and magnifiedB.Virtual, upright, and magnifiedC.Real, upright, and diminishedD.No image is formed when the object is inside the focal length.

Question 48

A diffraction grating with $500 lines/mm$ is illuminated with light of wavelength $λ = 600 nm$ . At what angle does the first-order ( $m = 1$ ) maximum appear?

θ \approx 17.5°

θ \approx 30°

θ \approx 8.6°

θ \approx 35.1°

Question 49

Which of the following best describes the zeroth law of thermodynamics?

A.Energy cannot be created or destroyed in an isolated system.B.If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.C.Heat flows spontaneously from cold objects to hot objects.D.The entropy of a perfect crystal at absolute zero is zero.

Question 50

A parallel-plate capacitor has plate area $A$ and plate separation $d$ . If the separation is doubled while the charge on the plates remains constant, how does the voltage across the capacitor change?

A.The voltage is halved.B.The voltage is unchanged.C.The voltage doubles.D.The voltage quadruples.

AP Physics 2 Full-length practice exam 1 — Free with Answer Explanations | Test Practice Hub