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POST UTME BELLS UNIVERSITY 2021 Physics | Objective

Are you preparing for POST UTME BELLS UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2021 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 $psi_1(x) = \sqrt{\frac{2}{L}} \sinleft$ \frac{pi x}{L}\right $$. What is the expectation value of the position operator for this state?

A. 0

Correct B. \frac{L}{2}

C. L

D. \frac{2L}{\pi}

Correct Answer: B

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Question 2

A magnetic field of magnitude $B$ is directed perp\endicular to the plane of a circular loop of radius $r$. The loop is made of a material with a magnetic susceptibility of $\chi$. What is the magnetic moment of the loop?

A. \frac{\pi r^2 B}{\mu_0}

Correct B. \chi \frac{\pi r^2 B}{\mu_0}

C. \frac{\chi \pi r^2 B}{\mu_0}

D. \frac{\pi r^2 B}{\mu_0 \chi}

Correct Answer: B

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Question 3

A resistor of resis\tance $R$ is connected in series with an inductor of induc\tance $L$. The circuit is driven by a \sinusoidal voltage source of amplitude $V_0$ and frequency $f$. What is the impedance of the circuit?

A. R

Correct B. \sqrt{R^2 + $ \omega L $^2}

C. \frac{R}{\omega L}

D. \frac{\omega L}{R}

Correct Answer: B

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Question 4

A heat engine operates between two temperatures $T_1$ and $T_2$. The engine has an efficiency of $\eta$. What is the ratio of the high-temperature reservoir to the low-temperature reservoir?

A. 1

B. 1 - \eta

Correct C. \frac{1}{1 - \eta}

D. \frac{1 - \eta}{\eta}

Correct Answer: C

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Question 5

A sound wave of frequency $f$ is traveling through a medium with a speed $v$. The wave has an amplitude $A$ and a wavelength $\lambda$. What is the period of the wave?

Correct A. \frac{2\pi}{f}

B. \frac{v}{f}

C. \frac{\lambda}{v}

D. \frac{v}{\lambda}

Correct Answer: A

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Question 6

A beam of light of wavelength 500 nm is incident on a glass slab of re\fractive index 1.5. If the angle of incidence is 30°, what is the angle of re\fraction?

Correct A. 20°

B. 30°

C. 40°

D. 50°

Correct Answer: A

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Question 7

A 100 W light bulb is connected to a 220 V power source. What is the current drawn by the bulb?

Correct A. 0.45 A

B. 0.5 A

C. 0.55 A

D. 0.6 A

Correct Answer: A

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Question 8

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

A. 10 N

B. 20 N

Correct C. 30 N

D. 40 N

Correct Answer: C

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Question 9

A wave of frequency 100 Hz and wavelength 2 m is traveling through a medium. What is the speed of the wave?

Correct A. 200 m/s

B. 400 m/s

C. 600 m/s

D. 800 m/s

Correct Answer: A

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Question 10

A 5 kg block is attached to a horizontal spring with a force cons\tant of 100 N/m. If the block is displaced by 2 m from its equilibrium position and released, what is the maximum speed of the block?

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 11

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

A. 20°

Correct B. 25°

C. 30°

D. 35°

Correct Answer: B

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Question 12

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. Calculate the magnitude of the force acting on the particle.

A. 16 N

B. 20 N

Correct C. 24 N

D. 28 N

Correct Answer: C

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Question 13

A circuit consists of a 12 V battery, a 4 Ω resistor, and a 6 Ω resistor connected in series. Calculate the total resis\tance and the current flowing through the circuit.

Correct A. 10 Ω, 1.2 A

B. 12 Ω, 1 A

C. 15 Ω, 0.8 A

D. 20 Ω, 0.6 A

Correct Answer: A

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Question 14

A wave has a frequency of 50 Hz and a wavelength of 0.2 m. Calculate the speed of the wave.

A. 5 m/s

Correct B. 10 m/s

C. 15 m/s

D. 20 m/s

Correct Answer: B

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Question 15

A particle of mass 1 kg is moving with a velocity of 5 m/s. Calculate the kinetic energy of the particle.

A. 10 J

Correct B. 12.5 J

C. 15 J

D. 20 J

Correct Answer: B

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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 force?

A. 10 N

Correct B. 12 N

C. 15 N

D. 18 N

Correct Answer: B

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Question 17

A circuit consists of a 12 V battery, a 4 Ω resistor, and an unknown resistor. If the current in the circuit is 2 A, what is the value of the unknown resistor?

A. 2 Ω

B. 4 Ω

Correct C. 6 Ω

D. 8 Ω

Correct Answer: C

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Question 18

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 acceleration of the body?

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 19

A spring has a spring cons\tant of 100 N/m. If a force of 50 N is applied to the spring, what is the displacement of the spring?

A. 0.5 m

Correct B. 1 m

C. 1.5 m

D. 2 m

Correct Answer: B

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Question 20

A particle of mass 3 kg is moving in a circular path of radius 2 m with a cons\tant speed of 6 m/s. If the particle is subjected to a centripetal force of 15 N, what is the magnitude of the force?

A. 10 N

B. 12 N

Correct C. 15 N

D. 18 N

Correct Answer: C

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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 subject to a centripetal force $F_c$ given by $F_c = \frac{mv^2}{r}$. If the particle's speed is doubled, what is the new centripetal force $F_c'$?

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

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

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

D. \frac{mv^2}{4r}

Correct Answer: A

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Question 22

A block of mass $m$ is placed on a frictionless surface and attached to a horizontal spring with a spring cons\tant $k$. The block is displaced by a dis\tance $x$ from its equilibrium position and released from rest. Assuming the block undergoes simple harmonic motion, what is the angular frequency $\omega$ of the motion?

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

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

C. \frac{k}{m}

D. \frac{m}{k}

Correct Answer: B

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Question 23

A sound wave with a frequency of $f$ is traveling through a medium with a speed $v$. If the wavelength of the sound wave is $\lambda$, what is the period $T$ of the sound wave?

A. \frac{v}{f}

B. \frac{\lambda}{f}

C. \frac{v}{f}

Correct D. \frac{\lambda}{v}

Correct Answer: D

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Question 24

A circuit consists of a resistor $R$, an inductor $L$, and a capacitor $C$ connected in series. The circuit is driven by a voltage source $V$ with a frequency $f$. If the impedance $Z$ of the circuit is given by $Z = \sqrt{R^2 + $ \omega L - \frac{1}{\omega C} $^2}$, what is the phase angle $\phi$ between the current $I$ and the voltage $V$?

Correct A. \arc\tan$ \frac{\omega L - \frac{1}{\omega C}}{R} $

B. \arc\tan$ \frac{R}{\omega L - \frac{1}{\omega C}} $

C. \arc\tan$ \frac{\omega L + \frac{1}{\omega C}}{R} $

D. \arc\tan$ \frac{R}{\omega L + \frac{1}{\omega C}} $

Correct Answer: A

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Question 25

A \tank is filled with water to a height $h$. The pressure at the bottom of the \tank is given by $P = \rho gh$, where $\rho$ is the density of water and $g$ is the acceleration due to gravity. If the density of water is $\rho = 1000 \text{ kg/m}^3$ and the acceleration due to gravity is $g = 9.8 \text{ m/s}^2$, what is the pressure at the bottom of the \tank?

Correct A. 9800 \text{ Pa}

B. 10000 \text{ Pa}

C. 98000 \text{ Pa}

D. 100000 \text{ Pa}

Correct Answer: A

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