Practice Post UTME ABU physics 2022 Past Questions

Question 1

A particle of mass $m$ is attached to a spring with spring cons\tant $k$. The particle is displaced by a dis\tance $x_0$ from its equilibrium position and released from rest. Assuming the motion is simple harmonic, find the angular frequency of the particle's motion.

Correct A. \sqrt{\frac{k}{m}}

B. \frac{k}{m}

C. \frac{m}{k}

D. \frac{1}{\sqrt{mk}}

Correct Answer: A

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Question 2

A circuit consists of a resistor $R$, an inductor $L$, and a capacitor $C$ connected in series. The circuit is driven by a \sinusoidal voltage source with amplitude $V_0$ and frequency $f$. Find the impedance of the circuit.

Correct A. \sqrt{R^2 + $ \omega L - \frac{1}{\omega C} $^2}

B. \frac{1}{\sqrt{R^2 + $ \omega L - \frac{1}{\omega C} $^2}}

C. \sqrt{R^2 - $ \omega L - \frac{1}{\omega C} $^2}

D. \frac{1}{\sqrt{R^2 - $ \omega L - \frac{1}{\omega C} $^2}}

Correct Answer: A

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Question 3

A wave with amplitude $A$ and frequency $f$ is propagating through a medium with speed $v$. Find the wavelength of the wave.

Correct A. \frac{v}{f}

B. \frac{f}{v}

C. \frac{A}{f}

D. \frac{v}{A}

Correct Answer: A

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Question 4

A sound wave with frequency $f$ is propagating through a medium with speed $v$. Find the time period of the wave.

Correct A. \frac{1}{f}

B. f

C. \frac{v}{f}

D. \frac{f}{v}

Correct Answer: A

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Question 5

A particle of mass $m$ is moving in a circular path with radius $r$ and angular speed $\omega$. Find the centripetal force acting on the particle.

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

B. \frac{mr^2}{v}

C. \frac{v^2}{mr}

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

Correct Answer: A

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Question 6

A particle of mass 2 kg is moving in a circular path of radius 3 m with a cons\tant speed of 4 m/s. If the particle is subjected to a centripetal force of 12 N, what is the magnitude of the acceleration of the particle?

A. 8 m/s^2

B. 12 m/s^2

Correct C. 16 m/s^2

D. 20 m/s^2

Correct Answer: C

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Question 7

A block of mass 5 kg is placed on a frictionless surface and attached to a horizontal spring with a force cons\tant of 200 N/m. If the block is displaced by 0.2 m from its equilibrium position and released from rest, what is the maximum speed of the block?

A. 1 m/s

Correct B. 2 m/s

C. 3 m/s

D. 4 m/s

Correct Answer: B

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Question 8

A ray of light passes from air into a glass of re\fractive index 1.5. If the angle of incidence is 30°, what is the angle of re\fraction?

A. 20°

B. 30°

Correct C. 41.8°

D. 50°

Correct Answer: C

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Question 9

A car travels from rest to a speed of 25 m/s in 10 s. What is the average acceleration of the car?

A. 1.5 m/s^2

B. 2 m/s^2

Correct C. 2.5 m/s^2

D. 3 m/s^2

Correct Answer: C

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Question 10

A block of mass 3 kg is attached to a horizontal spring with a force cons\tant of 100 N/m. If the block is displaced by 0.1 m from its equilibrium position and released from rest, what is the maximum speed of the block?

A. 0.5 m/s

Correct B. 1 m/s

C. 1.5 m/s

D. 2 m/s

Correct Answer: B

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Question 11

A block of mass 5 kg is susp\ended from a spring with spring cons\tant 200 N/m. If the block is displaced by 0.2 m from its equilibrium position and released, what is the maximum speed of the block?

A. 2 m/s

B. 4 m/s

Correct C. 6 m/s

D. 8 m/s

Correct Answer: C

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Question 12

A ray of light passes from air into a glass slab of re\fractive index 1.5. If the angle of incidence is 30°, what is the angle of re\fraction?

A. 20°

Correct B. 30°

C. 40°

D. 50°

Correct Answer: B

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Question 13

A 100 V AC supply is connected to a 50 Ω resistor. If the frequency of the supply is 50 Hz, what is the rms value of the current?

A. 1 A

Correct B. 2 A

C. 3 A

D. 4 A

Correct Answer: B

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Question 14

A heat engine operates between two reservoirs at temperatures 300 K and 500 K. If the efficiency of the engine is 30%, what is the work done per cycle?

A. 100 J

B. 200 J

Correct C. 300 J

D. 400 J

Correct Answer: C

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Question 15

A sound wave has a frequency of 200 Hz and a speed of 340 m/s. If the amplitude of the wave is 0.01 m, what is the intensity of the wave?

A. 10^-3 W/m^2

B. 10^-4 W/m^2

Correct C. 10^-5 W/m^2

D. 10^-6 W/m^2

Correct Answer: C

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Question 16

A particle of mass 2 kg is moving in a circular path of radius 3 m with a cons\tant speed of 4 m/s. If the particle is subjected to a centripetal force of 12 N, what is the magnitude of the acceleration of the particle?

Correct A. 6 m/s^2

B. 8 m/s^2

C. 10 m/s^2

D. 12 m/s^2

Correct Answer: A

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Question 17

A capacitor of capaci\tance 10 μF is connected in series with a resistor of resis\tance 20 Ω. If a voltage of 50 V is applied across the circuit, what is the current flowing through the circuit?

Correct A. 2.5 A

B. 5 A

C. 10 A

D. 20 A

Correct Answer: A

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Question 18

A wave of frequency 100 Hz and wavelength 2 m is propagating through a medium. If the wave is reflected from a fixed \end, what is the frequency of the reflected wave?

Correct A. 100 Hz

B. 200 Hz

C. 300 Hz

D. 400 Hz

Correct Answer: A

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Question 19

A block of mass 5 kg is moving with a speed of 10 m/s on a frictionless surface. If the block is subjected to a force of 20 N, what is the acceleration of the block?

Correct A. 4 m/s^2

B. 6 m/s^2

C. 8 m/s^2

D. 10 m/s^2

Correct Answer: A

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Question 20

A capacitor of capaci\tance 20 μF is connected in parallel with a resistor of resis\tance 10 Ω. If a voltage of 100 V is applied across the circuit, what is the current flowing through the capacitor?

Correct A. 10 A

B. 20 A

C. 30 A

D. 40 A

Correct Answer: A

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Question 21

A particle of mass 2 kg is moving in a circular path of radius 3 m with a cons\tant speed of 4 m/s. What is the magnitude of the centripetal force acting on the particle?

A. 20 N

B. 24 N

Correct C. 28 N

D. 32 N

Correct Answer: C

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Question 22

A capacitor consists of two parallel plates, each of area 0.04 m^2, separated by a dis\tance of 0.002 m. The capaci\tance of the capacitor is?

A. 0.02 F

Correct B. 0.04 F

C. 0.06 F

D. 0.08 F

Correct Answer: B

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Question 23

A projectile is launched from the ground with an initial velocity of 20 m/s at an angle of 60° above the horizontal. What is the maximum height reached by the projectile?

A. 10 m

B. 15 m

Correct C. 20 m

D. 25 m

Correct Answer: C

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Question 24

A radioactive sample decays at a rate of 0.05% per hour. If the initial activity of the sample is 1000 Bq, what is the activity after 5 hours?

A. 900 Bq

B. 950 Bq

C. 980 Bq

Correct D. 990 Bq

Correct Answer: D

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Question 25

A 10 μF capacitor is connected in series with a 20 Ω resistor. What is the time cons\tant of the circuit?

A. 0.2 s

Correct B. 0.4 s

C. 0.6 s

D. 0.8 s

Correct Answer: B

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