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POST UTME AL-HIKMAH UNIVERSITY 2025 Physics | Objective

Are you preparing for POST UTME AL-HIKMAH 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.

Practice these randomly selected questions to test your readiness.

Question 1

A particle of mass $m$ is moving in a circular orbit of radius $r$ under the influence of a central force given by $F(r) = \frac{k}{r^2}$, where $k$ is a cons\tant. If the particle's speed is $v$, what is its angular momentum?

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

B. \frac{mv}{k}

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

D. \frac{mv}{r}

Correct Answer: A

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Question 2

A gas is enclosed in a container with a movable piston. The gas is heated, cau\sing its pressure to increase. What is the effect on the gas's volume?

A. The volume decreases

Correct B. The volume increases

C. The volume remains cons\tant

D. The volume becomes zero

Correct Answer: B

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Question 3

A block of mass $m$ is attached to a horizontal, massless spring with spring cons\tant $k$. The block is displaced by a dis\tance $x$ and then released from rest. What is the block's angular frequency?

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 4

A radioactive sample has a half-life of $T_{1/2}$. If the initial activity is $A_0$, what is the activity after a time $t$?

Correct A. A_0 e^{-t/T_{1/2}}

B. A_0 e^{t/T_{1/2}}

C. A_0 + t/T_{1/2}

D. A_0 - t/T_{1/2}

Correct Answer: A

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Question 5

A projectile is launched from the origin with an initial velocity $v_0$ at an angle $\theta$ above the horizontal. What is the projectile's range?

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

B. \frac{v_0^2}{g} \cos 2\theta

C. \frac{v_0^2}{g} \sin \theta

D. \frac{v_0^2}{g} \cos \theta

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?

Correct A. 5.33 m/s^2

B. 10.66 m/s^2

C. 20 m/s^2

D. 30 m/s^2

Correct Answer: A

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Question 7

A 10 μF capacitor is connected in series with a 20 Ω resistor and a 5 V battery. If the switch is closed at t = 0, what is the charge on the capacitor after 5 seconds?

Correct A. 50 μC

B. 100 μC

C. 200 μC

D. 500 μC

Correct Answer: A

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Question 8

A wave with a frequency of 100 Hz and an amplitude of 2 m is traveling along a string. If the wave is reflected off a fixed \end, what is the amplitude of the reflected wave?

Correct A. -2 m

B. 0 m

C. 1 m

D. 2 m

Correct Answer: A

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Question 9

A 5 kg object is moving in a circular path of radius 2 m with a cons\tant speed of 3 m/s. If the object is subjected to a centripetal force of 10 N, what is the magnitude of the acceleration of the object?

Correct A. 4.5 m/s^2

B. 9 m/s^2

C. 18 m/s^2

D. 27 m/s^2

Correct Answer: A

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Question 10

A 10 μF capacitor is connected in parallel with a 20 Ω resistor and a 5 V battery. If the switch is closed at t = 0, what is the charge on the capacitor after 5 seconds?

Correct A. 50 μC

B. 100 μC

C. 200 μC

D. 500 μC

Correct Answer: A

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Question 11

A particle of mass 2 kg is projected from the origin with an initial velocity of 10 m/s at an angle of 60° to the horizontal. Assuming the acceleration due to gravity is 9.8 m/s², calculate the time taken for the particle to reach its maximum height.

A. 1.5 s

Correct B. 2.0 s

C. 2.5 s

D. 3.0 s

Correct Answer: B

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Question 12

A 12 V battery is connected in series with a 4 Ω resistor and a 6 Ω resistor. Calculate the current flowing through the circuit.

A. 1.5 A

B. 2.0 A

Correct C. 2.5 A

D. 3.0 A

Correct Answer: C

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Question 13

A gas occupies a volume of 2.5 L at a pressure of 1.5 atm and a temperature of 300 K. Calculate the volume occupied by the gas at a pressure of 2.0 atm and a temperature of 400 K.

A. 3.2 L

B. 3.5 L

Correct C. 4.0 L

D. 4.5 L

Correct Answer: C

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Question 14

A sound wave with a frequency of 200 Hz and a wavelength of 1.5 m is traveling through a medium with a speed of 340 m/s. Calculate the amplitude of the 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 15

A heat engine operates between a temperature of 500 K and a temperature of 300 K. Calculate the efficiency of the engine.

A. 0.4

B. 0.5

Correct C. 0.6

D. 0.7

Correct Answer: C

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Question 16

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 $psi_0(x) = \sqrt{\frac{2}{L}} \sinleft$ \frac{pi x}{L}\right $$. What is the expectation value of the position operator $hat{x}$ in the ground state?

A. 0

Correct B. \frac{L}{2}

C. L

D. \frac{L}{\pi}

Correct Answer: B

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Question 17

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 $x$ from its equilibrium position and released from rest. What is the angular frequency of the resulting simple harmonic motion?

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

B. \frac{k}{M}

C. \frac{M}{k}

D. \frac{\pi}{2}

Correct Answer: A

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Question 18

A ray of light passes from air into a medium with re\fractive index $n$. If the angle of incidence is $\theta_i$, what is the angle of re\fraction $\theta_r$?

Correct A. \frac{n}{n_{air}} \sin\theta_i

B. \frac{n_{air}}{n} \sin\theta_i

C. \sin\theta_i

D. \cos\theta_i

Correct Answer: A

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Question 19

A parallel plate capacitor has plates of area $A$ and separation $d$. If the capaci\tance is $C$, what is the charge on the plates when a potential difference of $V$ is applied?

Correct A. CV

B. \frac{CV}{2}

C. \frac{C}{V}

D. \frac{V}{C}

Correct Answer: A

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Question 20

A simple p\endulum of length $L$ has a bob of mass $m$. If the p\endulum is released from an angle $\theta$ from the vertical, what is the time period $T$?

Correct A. 2\pi \sqrt{\frac{L}{g}}

B. \frac{L}{g}

C. \frac{g}{L}

D. \frac{\pi}{2}

Correct Answer: A

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Question 21

A particle of mass $m$ is moving in a circular path of radius $r$ with a cons\tant speed $v$. The particle is subjected to a centripetal force $F_c = \frac{mv^2}{r}$. If the particle is moving in a clockwise direction, what is the direction of the force $F_c$?

Correct A. towards the center

B. away from the center

C. perp\endicular to the radius

D. along the radius

Correct Answer: A

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Question 22

A wave of wavelength $\lambda$ and frequency $f$ is traveling through a medium with speed $v$. If the wave is reflected from a fixed \end, what is the new wavelength of the wave?

Correct A. \frac{\lambda}{2}

B. \frac{\lambda}{4}

C. \frac{\lambda}{3}

D. \frac{\lambda}{5}

Correct Answer: A

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Question 23

A quantum particle of mass $m$ is confined to a one-dimensional box of length $L$. The particle is in the ground state, and its wave function is given by $\psi(x) = \sqrt{\frac{2}{L}} \sin\left$ \frac{\pi x}{L}\right $$. What is the expectation value of the particle's position?

Correct A. \frac{L}{2}

B. \frac{L}{4}

C. \frac{3L}{4}

D. L

Correct Answer: A

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Question 24

A rigid rod of length $L$ is fixed at one \end and free at the other \end. The rod is subjected to a force $F$ at the free \end, cau\sing it to rotate about the fixed \end. What is the torque $\tau$ exerted on the rod?

Correct A. FL

B. \frac{FL}{2}

C. \frac{FL}{3}

D. \frac{FL}{4}

Correct Answer: A

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Question 25

A heat engine operates between two temperatures $T_1$ and $T_2$, where $T_1 > T_2$. The engine has an efficiency $\eta$ given by $\eta = 1 - \frac{T_2}{T_1}$. What is the maximum possible efficiency of the engine?

Correct A. 1

B. \frac{T_2}{T_1}

C. 1 - \frac{T_2}{T_1}

D. \frac{T_1}{T_2}

Correct Answer: A

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