Practice Post UTME NILE UNIVERSITY physics 2024 Past Questions

Question 1

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

A. ω = 0

Correct B. ω = √$ k/m $

C. ω = k/m

D. ω = √$ m/k $

Correct Answer: B

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Question 2

A light ray passes from air into a glass slab of re\fractive index $n$. If the angle of incidence is $θ_i$, what is the angle of re\fraction $θ_r$?

Correct A. θ_r = θ_i/n

B. θ_r = nθ_i

C. θ_r = θ_i - n

D. θ_r = n - θ_i

Correct Answer: A

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Question 3

A sound wave with frequency $f$ is produced by a source moving at a speed $v_s$. If the speed of sound in the medium is $v$, what is the Doppler shift $Δf$?

A. Δf = f - v_s/v

Correct B. Δf = f + v_s/v

C. Δf = v_s/vf

D. Δf = fv_s/v

Correct Answer: B

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Question 4

A particle of mass $m$ is in a one-dimensional potential well of depth $V_0$. If the particle is in the ground state, what is the expectation value of its position $<x>$?

Correct A. = a/2

B. = a

C. = 2a

D. = 3a

Correct Answer: A

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Question 5

A beam of light passes through a convex lens of focal length $f$. If the object dis\tance is $u$, what is the image dis\tance $v$?

Correct A. 1/v = 1/f - 1/u

B. 1/v = 1/f + 1/u

C. 1/v = 1/f - u

D. 1/v = 1/f + u

Correct Answer: A

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Question 6

A parallel plate capacitor has a capaci\tance of 10 μF and is charged to a potential difference of 12 V. If the dis\tance between the plates is doubled, what is the new capaci\tance?

A. 5 μF

B. 20 μF

C. 10 μF

Correct D. 2.5 μF

Correct Answer: D

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Question 7

A 2 kg block is attached to a horizontal, massless spring with a force cons\tant of 100 N/m. 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. 0.5 m/s

B. 1.0 m/s

Correct C. 1.5 m/s

D. 2.0 m/s

Correct Answer: C

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Question 8

A heat engine operates between two reservoirs at temperatures 400 K and 300 K. The engine has an efficiency of 30%. What is the temperature of the hot reservoir?

A. 500 K

B. 600 K

Correct C. 700 K

D. 800 K

Correct Answer: C

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Question 9

A circuit consists of a 10 Ω resistor, a 20 Ω resistor, and a 30 Ω resistor connected in series. What is the equivalent resis\tance of the circuit?

A. 50 Ω

B. 60 Ω

Correct C. 70 Ω

D. 80 Ω

Correct Answer: C

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Question 10

A projectile is launched from the ground with an initial velocity of 20 m/s at an angle of 30° above the horizontal. What is the maximum height reached by the projectile?

A. 5 m

B. 10 m

Correct C. 15 m

D. 20 m

Correct Answer: C

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Question 11

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. 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 12

A 100 W light bulb is connected to a 220 V power source. If the resis\tance of the bulb is 10 ohms, what is the current flowing through the bulb?

A. 0.5 A

Correct B. 1 A

C. 2 A

D. 4 A

Correct Answer: B

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Question 13

A wave with a frequency of 50 Hz and a wavelength of 2 m is traveling through a medium. If the speed of the wave is 100 m/s, what is the amplitude of the wave?

A. 0.1 m

B. 0.2 m

C. 0.3 m

Correct D. 0.4 m

Correct Answer: D

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Question 14

A body of mass 5 kg is moving with a velocity of 10 m/s. If the body is subjected to a force of 20 N, what is the change in its kinetic energy?

A. 100 J

Correct B. 200 J

C. 300 J

D. 400 J

Correct Answer: B

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Question 15

A simple harmonic motion has a frequency of 2 Hz and an amplitude of 0.5 m. If the initial phase angle is 30 degrees, what is the equation of the motion?

Correct A. x(t) = 0.5\sin$ 4\pi t + \frac{\pi}{6} $

B. x(t) = 0.5\sin$ 4\pi t - \frac{\pi}{6} $

C. x(t) = 0.5\cos$ 4\pi t + \frac{\pi}{6} $

D. x(t) = 0.5\cos$ 4\pi t - \frac{\pi}{6} $

Correct Answer: A

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Question 16

A 2 kg block of ice at 0°C is placed in a 10°C water bath. Assuming the specific heat capacity of ice is 2090 J/(kg°C) and the latent heat of fusion of ice is 334 kJ/kg, calculate the energy required to melt the ice completely.

A. 2.1 kJ

Correct B. 3.4 kJ

C. 4.2 kJ

D. 5.5 kJ

Correct Answer: B

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Question 17

A particle of mass 0.5 kg is moving in a circular path of radius 2 m with a cons\tant speed of 4 m/s. If the particle is subjected to a centripetal force of 10 N, calculate the time taken for the particle to complete one revolution.

A. 1.6 s

Correct B. 2.1 s

C. 2.5 s

D. 3.2 s

Correct Answer: B

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Question 18

A 100 Ω resistor is connected in series with a 20 μF capacitor and a 10 μH inductor. If the circuit is driven by a 50 Hz AC source with a peak voltage of 10 V, calculate the impedance of the circuit.

A. 150 Ω

B. 200 Ω

Correct C. 250 Ω

D. 300 Ω

Correct Answer: C

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Question 19

A magnetic field of 0.5 T is applied to a coil of 100 turns and a radius of 0.1 m. If the coil is rotated at a frequency of 50 Hz, calculate the induced emf in the coil.

A. 1.6 V

B. 2.1 V

Correct C. 2.5 V

D. 3.2 V

Correct Answer: C

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Question 20

A 10 μF capacitor is connected in parallel with a 100 Ω resistor. If the circuit is driven by a 50 Hz AC source with a peak voltage of 10 V, calculate the current through the resistor.

A. 0.1 A

Correct B. 0.2 A

C. 0.3 A

D. 0.4 A

Correct Answer: B

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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. If the particle is subjected to a centripetal force of 12 N, what is the magnitude of the acceleration of the particle?

A. 10 m/s^2

Correct B. 12 m/s^2

C. 15 m/s^2

D. 20 m/s^2

Correct Answer: B

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Question 22

A parallel plate capacitor has a capaci\tance of 5 μF. If a potential difference of 10 V is applied across the plates, what is the charge stored on the capacitor?

A. 0.05 C

Correct B. 0.1 C

C. 0.5 C

D. 1 C

Correct Answer: B

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Question 23

A body of mass 5 kg is moving with a velocity of 2 m/s. If it is subjected to a force of 10 N, what is the acceleration of the body?

A. 0.5 m/s^2

B. 1 m/s^2

C. 2 m/s^2

Correct D. 5 m/s^2

Correct Answer: D

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Question 24

A spring has a spring cons\tant of 100 N/m. If it is stretched by 2 m, what is the potential energy stored in the spring?

A. 200 J

Correct B. 400 J

C. 600 J

D. 800 J

Correct Answer: B

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Question 25

A particle of mass 3 kg is moving in a circular path of radius 4 m with a cons\tant speed of 3 m/s. If the particle is subjected to a centripetal force of 15 N, what is the magnitude of the acceleration of the particle?

A. 10 m/s^2

B. 12 m/s^2

Correct C. 15 m/s^2

D. 20 m/s^2

Correct Answer: C

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