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POST UTME RSU 2023 Physics | Objective

Are you preparing for POST UTME RSU exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2023 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 $L$. If the particle is in the ground state, what is the expectation value of its position?

Correct A. \frac{L}{2}

B. \frac{L}{4}

C. \frac{3L}{4}

D. \frac{L}{\pi}

Correct Answer: A

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Question 2

A heat engine operates between two reservoirs at temperatures $T_1 = 500 \text{ K}$ and $T_2 = 300 \text{ K}$. If the engine produces 1000 J of work per cycle, what is its efficiency?

Correct A. 0.4

B. 0.5

C. 0.6

D. 0.7

Correct Answer: A

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Question 3

A sound wave with frequency $f = 200 \text{ Hz}$ is traveling through a medium with speed $v = 340 \text{ m/s}$. If the wave is reflected off a stationary surface, what is the frequency of the reflected wave?

Correct A. 200 Hz

B. 400 Hz

C. 600 Hz

D. 800 Hz

Correct Answer: A

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Question 4

A magnetic field $\vec{B} = $ 2 \text{ T} $ \hat{x}$ is applied to a current-carrying wire. If the wire has a current $I = 5 \text{ A}$ and a length $L = 1 \text{ m}$, what is the force exerted on the wire?

A. 10 N

Correct B. 20 N

C. 30 N

D. 40 N

Correct Answer: B

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Question 5

A unit of length is defined as the dis\tance between two consecutive crests of a wave. If the wavelength of the wave is $\lambda = 2 \text{ m}$, what is the unit of length?

A. 1 m

Correct B. 2 m

C. 3 m

D. 4 m

Correct Answer: B

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Question 6

A parallel plate capacitor has a capaci\tance of 2 μF. If a potential difference of 10 V is applied across it, what is the charge stored on the plates?

A. 20 μC

Correct B. 40 μC

C. 60 μC

D. 80 μC

Correct Answer: B

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Question 7

A block of mass 5 kg is attached to a horizontal spring with a spring 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 its angular frequency?

A. 2 rad/s

B. 4 rad/s

Correct C. 6 rad/s

D. 8 rad/s

Correct Answer: C

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Question 8

A current of 2 A flows through a resistor of 10 Ω. If the voltage across the resistor is 20 V, what is the power dissipated in the resistor?

Correct A. 40 W

B. 80 W

C. 120 W

D. 160 W

Correct Answer: A

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Question 9

A capacitor of 100 μF is charged to a potential difference of 50 V. If it is then connected to a resistor of 500 Ω, what is the time cons\tant of the circuit?

A. 0.1 s

B. 0.2 s

Correct C. 0.5 s

D. 1 s

Correct Answer: C

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Question 10

A block of mass 10 kg is moving with a velocity of 5 m/s. If it is brought to rest by a force of 20 N, what is the dis\tance traveled by the block?

A. 2 m

B. 4 m

Correct C. 6 m

D. 8 m

Correct Answer: C

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Question 11

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 potential difference?

A. 6 V

B. 12 V

Correct C. 24 V

D. 48 V

Correct Answer: C

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Question 12

A current of 2 A flows through a resistor of 4 Ω. What is the power dissipated by the resistor?

A. 8 W

Correct B. 16 W

C. 32 W

D. 64 W

Correct Answer: B

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Question 13

A \sinusoidal voltage source has a maximum voltage of 20 V and a frequency of 50 Hz. What is the rms voltage?

A. 10 V

Correct B. 14.14 V

C. 20 V

D. 28.28 V

Correct Answer: B

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Question 14

A particle moves in a circular path with a radius of 2 m and a frequency of 3 Hz. What is the angular frequency?

A. 6 rad/s

Correct B. 12 rad/s

C. 18 rad/s

D. 24 rad/s

Correct Answer: B

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Question 15

A gas expands from 1 L to 2 L against a cons\tant external pressure of 2 atm. What is the work done?

A. -4 J

B. -2 J

Correct C. 2 J

D. 4 J

Correct Answer: C

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Question 16

A beam 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. 25°

C. 30°

D. 35°

Correct Answer: B

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Question 17

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 18

A 2 kg block is placed on a horizontal surface with a coefficient of friction of 0.5. If a force of 10 N is applied to the block, what is the acceleration of the block?

A. 0.5 m/s^2

Correct B. 1 m/s^2

C. 2 m/s^2

D. 5 m/s^2

Correct Answer: B

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Question 19

A heat engine operates between a source at 500 K and a \sink at 300 K. If the efficiency of the engine is 30%, what is the temperature of the source?

A. 400 K

B. 500 K

Correct C. 600 K

D. 700 K

Correct Answer: C

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Question 20

A magnetic field of 0.5 T is applied to a current-carrying wire of length 1 m. If the current is 2 A, what is the force on the wire?

A. 0.1 N

Correct B. 0.5 N

C. 1 N

D. 2 N

Correct Answer: B

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Question 21

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 $omega$ in terms of $k$ and $m$.

A. \omega = \frac{k}{m}

B. \omega = \sqrt{\frac{m}{k}}

C. \omega = \frac{m}{k}

Correct D. \omega = \sqrt{\frac{k}{m}}

Correct Answer: D

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Question 22

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

A. \theta_r = \theta_i

B. \theta_r = \frac{n}{\theta_i}

C. \theta_r = \frac{\theta_i}{n}

Correct D. \theta_r = \frac{\sin \theta_i}{n}

Correct Answer: D

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Question 23

A circuit consists of a resistor $R$, an inductor $L$, and a capacitor $C$ connected in series. If the circuit is driven by a voltage source $V_0$ with frequency $f$, what is the impedance $Z$ of the circuit?

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

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

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

D. Z = \sqrt{R^2 + $ \omega L + \frac{1}{\omega C} $^2} + \frac{1}{\omega C}

Correct Answer: A

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Question 24

A quantum 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 energy $E_1$ of the particle?

Correct A. E_1 = \frac{\pi^2 \hbar^2}{2mL^2}

B. E_1 = \frac{2\pi^2 \hbar^2}{mL^2}

C. E_1 = \frac{3\pi^2 \hbar^2}{2mL^2}

D. E_1 = \frac{4\pi^2 \hbar^2}{mL^2}

Correct Answer: A

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Question 25

A gas of molecules with mass $m$ and charge $q$ is confined to a box of volume $V$. If the temperature of the gas is $T$, what is the pressure $P$ exerted by the gas?

Correct A. P = \frac{2}{3} \frac{NkT}{V}

B. P = \frac{NkT}{V}

C. P = \frac{3}{2} \frac{NkT}{V}

D. P = \frac{5}{3} \frac{NkT}{V}

Correct Answer: A

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