Practice post utme abu physics 2021 Past Questions

Question 1

A particle of mass $m$ is moving in a circular path of radius $r$ with a cons\tant speed $v$. The particle is subject to a centripetal force $F_c$ given by $F_c = \frac{mv^2}{r}$. If the particle's speed is doubled, what happens to the centripetal force?

A. The centripetal force remains the same.

B. The centripetal force increases by a factor of 2.

Correct C. The centripetal force increases by a factor of 4.

D. The centripetal force decreases by a factor of 2.

Correct Answer: C

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Question 2

A block of mass $M$ is placed on a horizontal, frictionless surface. A horizontal force $F$ is applied to the block, cau\sing it to accelerate at a rate $a$. If the force is doubled, what happens to the acceleration?

A. The acceleration remains the same.

B. The acceleration increases by a factor of 2.

Correct C. The acceleration increases by a factor of 4.

D. The acceleration decreases by a factor of 2.

Correct Answer: C

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Question 3

A parallel plate capacitor has a capaci\tance $C$ and is charged to a potential difference $V$. If the dis\tance between the plates is doubled, what happens to the capaci\tance?

A. The capaci\tance remains the same.

B. The capaci\tance increases by a factor of 2.

C. The capaci\tance increases by a factor of 4.

Correct D. The capaci\tance decreases by a factor of 2.

Correct Answer: D

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Question 4

A simple harmonic oscillator has a frequency $f$ and is driven by a force $F$. If the amplitude of the oscillator is doubled, what happens to the maximum kinetic energy?

A. The maximum kinetic energy remains the same.

B. The maximum kinetic energy increases by a factor of 2.

Correct C. The maximum kinetic energy increases by a factor of 4.

D. The maximum kinetic energy decreases by a factor of 2.

Correct Answer: C

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Question 5

A fluid of density $\rho$ is flowing through a pipe of radius $R$ with a velocity $v$. If the velocity is doubled, what happens to the volume flow rate?

A. The volume flow rate remains the same.

B. The volume flow rate increases by a factor of 2.

Correct C. The volume flow rate increases by a factor of 4.

D. The volume flow rate decreases by a factor of 2.

Correct Answer: C

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Question 6

A gas is enclosed in a container with a movable piston. The gas is heated, cau\sing its pressure to increase. Which of the following statements is true about the behavior of the gas?

Correct A. The gas expands to fill the container.

B. The gas contracts to occupy less space.

C. The gas remains at cons\tant pressure.

D. The gas undergoes a phase transition.

Correct Answer: A

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Question 7

A particle of mass 2 kg is moving in a circular path with a radius of 3 m. If the particle's speed is 4 m/s, what is the magnitude of the centripetal acceleration?

A. 2 m/s^2

B. 4 m/s^2

Correct C. 6 m/s^2

D. 8 m/s^2

Correct Answer: C

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Question 8

A charged particle is moving through a magnetic field. If the particle's velocity is perp\endicular to the magnetic field, what is the direction of the force exerted on the particle?

A. Along the direction of the magnetic field.

B. Perp\endicular to the magnetic field.

C. Opposite to the direction of the magnetic field.

Correct D. In the direction of the velocity.

Correct Answer: D

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Question 9

A capacitor consists of two parallel plates separated by a dis\tance of 2 mm. If the capaci\tance is 10 μF, what is the charge stored on the capacitor when a potential difference of 5 V is applied?

A. 50 μC

Correct B. 100 μC

C. 200 μC

D. 500 μC

Correct Answer: B

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Question 10

A photon of energy 2 eV is incident on a metal surface. If the work function of the metal is 1.5 eV, what is the maximum kinetic energy of the emitted electron?

Correct A. 0.5 eV

B. 1 eV

C. 1.5 eV

D. 2 eV

Correct Answer: A

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Question 11

A particle of mass $m$ is moving in a circular path of radius $r$ with a cons\tant speed $v$. The particle experiences a centripetal force $F_c$ given by $F_c = \frac{mv^2}{r}$. If the particle's speed is doubled to $2v$, what is the new centripetal force $F_{c,new}$?

Correct A. \frac{2mv^2}{r}

B. \frac{mv^2}{2r}

C. \frac{mv^2}{r}

D. \frac{mv^2}{4r}

Correct Answer: A

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Question 12

A circuit consists of a $10\Omega$ resistor, a $5\mu F$ capacitor, and a $20\mu H$ inductor connected in series. If the circuit is driven by a $10\sin$ 2\pi ft $$ voltage source, what is the resonant frequency $f$?

A. 100\,Hz

B. 200\,Hz

Correct C. 500\,Hz

D. 1000\,Hz

Correct Answer: C

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Question 13

A radioactive sample has a half-life of $10$ years. If the initial activity is $100\,Bq$, what is the activity after $20$ years?

Correct A. 12.5\,Bq

B. 25\,Bq

C. 50\,Bq

D. 100\,Bq

Correct Answer: A

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Question 14

A heat engine operates between a high-temperature reservoir at $500\,K$ and a low-temperature reservoir at $300\,K$. If the engine has an efficiency of $30\%$, what is the maximum possible work output?

A. 500\,J

Correct B. 750\,J

C. 1000\,J

D. 1500\,J

Correct Answer: B

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Question 15

A particle of mass $m$ is moving in a circular path of radius $r$ with a cons\tant speed $v$. The particle experiences a centripetal force $F_c$ given by $F_c = \frac{mv^2}{r}$. If the particle's speed is doubled to $2v$, what is the new centripetal force $F_{c,new}$?

Correct A. \frac{2mv^2}{r}

B. \frac{mv^2}{2r}

C. \frac{mv^2}{r}

D. \frac{mv^2}{4r}

Correct Answer: A

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Question 16

A uniform magnetic field of magnitude 2 T is directed along the z-axis. A current of 5 A flows in a circular loop of radius 0.1 m, placed in the x-y plane. What is the magnitude of the magnetic moment of the loop?

A. 0.5 A m^2

B. 1 A m^2

Correct C. 2 A m^2

D. 5 A m^2

Correct Answer: C

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Question 17

A 10 Ω resistor is connected in series with a 20 Ω resistor and a 30 Ω resistor. If a voltage of 12 V is applied across the circuit, what is the current flowing through the 10 Ω resistor?

A. 0.4 A

Correct B. 0.6 A

C. 0.8 A

D. 1 A

Correct Answer: B

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Question 18

A gas at a pressure of 2 atm and a temperature of 300 K is allowed to expand to a volume of 5 m^3. What is the final pressure of the gas?

A. 0.8 atm

B. 1 atm

Correct C. 1.2 atm

D. 1.5 atm

Correct Answer: C

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Question 19

A block of mass 5 kg is attached to a spring with a spring cons\tant of 100 N/m. If the block is displaced by 0.2 m from its equilibrium position and released, what is the maximum velocity of the block?

A. 0.5 m/s

B. 1 m/s

Correct C. 1.5 m/s

D. 2 m/s

Correct Answer: C

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Question 20

A sound wave with a frequency of 200 Hz and a wavelength of 0.5 m is traveling through a medium with a speed of 340 m/s. What is the amplitude of the sound wave?

A. 0.05 m

Correct B. 0.1 m

C. 0.15 m

D. 0.2 m

Correct Answer: B

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Question 21

A particle of mass $m$ is confined to a one-dimensional box of length $L$. If the particle is in the ground state, what is the expectation value of its position?

A. 0

Correct B. +\frac{L}{2}

C. -\frac{L}{2}

D. L

Correct Answer: B

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Question 22

A projectile is launched from the origin with an initial velocity $v_0$ at an angle $\theta$ above the horizontal. If the projectile lands at a dis\tance $R$ from the origin, what is the time of flight?

Correct A. \frac{2v_0\sin\theta}{g}

B. \frac{v_0\sin\theta}{g}

C. \frac{2v_0\cos\theta}{g}

D. \frac{v_0\cos\theta}{g}

Correct Answer: A

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Question 23

A block of mass $m$ is attached to a horizontal spring with spring cons\tant $k$. If the block is displaced by a dis\tance $x$ from its equilibrium position and released, what is the maximum speed of the block?

Correct A. \sqrt{\frac{kx^2}{m}}

B. \sqrt{\frac{mx^2}{k}}

C. \sqrt{\frac{k}{m}}

D. \sqrt{\frac{m}{k}}

Correct Answer: A

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Question 24

A point charge $q$ is placed at the center of a spherical shell of radius $R$. If a test charge $Q$ is placed at a dis\tance $r$ from the center of the shell, what is the electric potential at the location of the test charge?

Correct A. \frac{1}{4\pi\epsilon_0}\frac{q}{r}

B. \frac{1}{4\pi\epsilon_0}\frac{q}{R}

C. \frac{1}{4\pi\epsilon_0}\frac{Q}{r}

D. \frac{1}{4\pi\epsilon_0}\frac{Q}{R}

Correct Answer: A

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Question 25

A parallel-plate capacitor has plates of area $A$ and separation $d$. If a charge $Q$ is placed on one plate, what is the electric field between the plates?

A. \frac{Q}{\epsilon_0A}

Correct B. \frac{Q}{\epsilon_0d}

C. \frac{Q}{\epsilon_0A^2}

D. \frac{Q}{\epsilon_0d^2}

Correct Answer: B

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