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POST UTME LEAD CITY UNIVERSITY 2025 Physics | Objective

Are you preparing for POST UTME LEAD CITY UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2025 Physics (Objective) questions designed to simulate the real exam environment.

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Question 1

A particle of mass m is confined to a one-dimensional box of length L. The ground state wave function of the particle is given by ψ(x) = √\( 2/L \) \sin\( πx/L \). What is the expectation value of the position operator x?

A. 0

Correct B. L/2

C. L

D. πL/2

Correct Answer: B

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Question 2

A radioactive sample decays according to the equation N(t) = N0e^\( -λt \), where N(t) is the number of nuclei remaining at time t, N0 is the initial number of nuclei, λ is the decay cons\tant, and t is time. If the half-life of the sample is 10 minutes, what is the decay cons\tant λ?

A. 0.0693 min^\( -1 \)

Correct B. 0.693 min^\( -1 \)

C. 6.93 min^\( -1 \)

D. 69.3 min^\( -1 \)

Correct Answer: B

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Question 3

A sound wave with frequency 200 Hz and amplitude 0.5 m is traveling through a medium with speed 343 m/s. What is the intensity of the sound wave?

A. 10^\( -3 \) W/m^2

B. 10^\( -2 \) W/m^2

Correct C. 10^\( -1 \) W/m^2

D. 10^0 W/m^2

Correct Answer: C

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Question 4

A particle of mass m is moving in a circular path of radius r with a cons\tant speed v. What is the magnitude of the net force acting on the particle?

A. 0

Correct B. mv^2/r

C. 2mv^2/r

D. mv^2/2r

Correct Answer: B

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Question 5

A block of mass m is placed on a frictionless surface and connected to a horizontal spring with spring cons\tant k. The block is displaced by a dis\tance x and released from rest. What is the maximum speed of the block?

A. 0

B. √\( kx/m \)

Correct C. √\( 2kx/m \)

D. √\( 3kx/m \)

Correct Answer: C

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Question 6

A block of mass 2 kg 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. Assuming the block undergoes simple harmonic motion, calculate the maximum speed of the block as it passes through the equilibrium position.

A. 2 m/s

Correct B. 4 m/s

C. 6 m/s

D. 8 m/s

Correct Answer: B

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Question 7

A particle of mass 1 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 12 N, determine the angle between the force and the radius vector.

A. 30°

B. 45°

Correct C. 60°

D. 90°

Correct Answer: C

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Question 8

A projectile is launched from the ground with an initial velocity of 20 m/s at an angle of 60° above the horizontal. If air resis\tance is neglected, determine the time of flight and the maximum height reached by the projectile.

A. 4 s, 10 m

B. 6 s, 15 m

Correct C. 8 s, 20 m

D. 10 s, 25 m

Correct Answer: C

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Question 9

A heat engine operates between two reservoirs at temperatures 500 K and 300 K. If the engine produces 100 J of work per cycle, determine the efficiency of the engine.

A. 20%

Correct B. 30%

C. 40%

D. 50%

Correct Answer: B

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Question 10

A quantum particle of mass 1 kg is confined to a one-dimensional box of length 1 m. If the particle is in the ground state, determine the probability of finding the particle in the left half of the box.

A. 25%

Correct B. 50%

C. 75%

D. 90%

Correct Answer: B

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Question 11

A light ray 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. 25°

C. 30°

D. 35°

Correct Answer: B

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Question 12

A 100 Ω resistor is connected in series with a 200 Ω resistor and a 50 Ω resistor. What is the total resis\tance?

A. 400 Ω

B. 450 Ω

Correct C. 500 Ω

D. 550 Ω

Correct Answer: C

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Question 13

A sound wave has a frequency of 200 Hz and a wavelength of 1.5 m. What is the speed of the sound wave?

A. 300 m/s

B. 400 m/s

Correct C. 500 m/s

D. 600 m/s

Correct Answer: C

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Question 14

A light ray passes through a convex lens of focal length 20 cm. If the object dis\tance is 30 cm, what is the image dis\tance?

A. 10 cm

B. 15 cm

Correct C. 20 cm

D. 25 cm

Correct Answer: C

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Question 15

A 10 V battery is connected in series with a 20 Ω resistor and a 30 Ω resistor. What is the current in the circuit?

A. 0.5 A

B. 1 A

Correct C. 1.5 A

D. 2 A

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. 5.33 m/s^2

B. 6.66 m/s^2

C. 8 m/s^2

D. 10 m/s^2

Correct Answer: A

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Question 17

A light ray 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. 30°

Correct B. 41.41°

C. 45°

D. 60°

Correct Answer: B

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Question 18

A 100 Ω resistor is connected in series with a 20 μF capacitor and a 50 mH inductor. If the circuit is driven by a 10 V AC source, what is the impedance of the circuit?

A. 100 Ω

Correct B. 103.94 Ω

C. 105 Ω

D. 110 Ω

Correct Answer: B

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Question 19

A 2 kg block is attached to a horizontal, massless spring with a force cons\tant of 100 N/m. If the block is displaced by 0.5 m from its equilibrium position and released from rest, what is the maximum speed of the block?

Correct A. 5.66 m/s

B. 6.66 m/s

C. 8 m/s

D. 10 m/s

Correct Answer: A

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Question 20

A 100 W light bulb is connected to a 220 V AC source. If the power factor is 0.8, what is the current drawn by the bulb?

Correct A. 0.625 A

B. 0.75 A

C. 0.875 A

D. 1 A

Correct Answer: A

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Question 21

A parallel plate capacitor has plates of area 0.04 m^2 and separation 0.02 m. If a potential difference of 10 V is applied across the plates, calculate the capaci\tance.

A. 2.5 x 10^-11 F

Correct B. 5 x 10^-11 F

C. 1 x 10^-10 F

D. 2 x 10^-10 F

Correct Answer: B

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Question 22

A particle of mass 2 kg is moving in a circular path of radius 3 m with a speed of 4 m/s. Calculate the centripetal force acting on the particle.

A. 16 N

B. 32 N

Correct C. 48 N

D. 64 N

Correct Answer: C

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Question 23

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

Correct A. 20°

B. 30°

C. 40°

D. 50°

Correct Answer: A

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Question 24

A particle of mass 1 kg is moving in a straight line with an initial velocity of 5 m/s. If a force of 2 N is applied in the opposite direction, calculate the acceleration after 2 seconds.

A. 1 m/s^2

Correct B. 2 m/s^2

C. 3 m/s^2

D. 4 m/s^2

Correct Answer: B

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Question 25

A parallel plate capacitor has plates of area 0.04 m^2 and separation 0.02 m. If a potential difference of 10 V is applied across the plates, calculate the energy stored in the capacitor.

A. 2.5 x 10^-10 J

Correct B. 5 x 10^-10 J

C. 1 x 10^-9 J

D. 2 x 10^-9 J

Correct Answer: B

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