Practice Post UTME COAL CITY UNIVERSITY physics 2025 Past Questions

Question 1

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 2

A circuit consists of a 12 V battery, a 4 Ω resistor, and an inductor of 2 H in series. If the current in the circuit is 2 A, what is the voltage drop across the inductor?

A. 8 V

B. 10 V

Correct C. 12 V

D. 14 V

Correct Answer: C

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Question 3

A radioactive sample has a half-life of 5 years. If the initial activity of the sample is 1000 Bq, what is the activity of the sample after 10 years?

A. 250 Bq

Correct B. 500 Bq

C. 750 Bq

D. 1000 Bq

Correct Answer: B

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Question 4

A heat engine operates between a high-temperature reservoir at 500 K and a low-temperature reservoir at 300 K. If the engine has an efficiency of 30%, what is the maximum possible work output of the engine?

A. 1000 J

B. 1500 J

Correct C. 2000 J

D. 2500 J

Correct Answer: C

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Question 5

A magnetic field of 2 T is applied to a current-carrying wire of length 1 m. If the current in the wire is 5 A, what is the force experienced by the wire?

A. 10 N

B. 15 N

Correct C. 20 N

D. 25 N

Correct Answer: C

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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?

A. 6 m/s^2

Correct B. 12 m/s^2

C. 18 m/s^2

D. 24 m/s^2

Correct Answer: B

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Question 7

A capacitor consists of two parallel plates, each of area 0.01 m^2, separated by a dis\tance of 0.001 m. If the capaci\tance of the capacitor is 10^-6 F, what is the charge stored on the capacitor when a potential difference of 100 V is applied across it?

Correct A. 10^-4 C

B. 10^-3 C

C. 10^-2 C

D. 10^-1 C

Correct Answer: A

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Question 8

A radioactive sample decays at a rate of 0.05% per hour. If the initial mass of the sample is 100 g, what is the mass of the sample after 5 hours?

Correct A. 90.2 g

B. 92.3 g

C. 94.5 g

D. 96.7 g

Correct Answer: A

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Question 9

A projectile is launched from the ground with an initial velocity of 20 m/s at an angle of 60° above the horizontal. If the acceleration due to gravity is 9.8 m/s^2, what is the maximum height reached by the projectile?

Correct A. 17.32 m

B. 20 m

C. 22.65 m

D. 25 m

Correct Answer: A

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Question 10

A wave has a frequency of 50 Hz and a wavelength of 0.02 m. If the wave is traveling in the positive x-direction, what is the speed of the wave?

Correct A. 1 m/s

B. 2 m/s

C. 3 m/s

D. 4 m/s

Correct Answer: A

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Question 11

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 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 12

A series RLC circuit has a resis\tance of $R = 10\,\Omega$, an induc\tance of $L = 0.1\,H$, and a capaci\tance of $C = 10^{-6}\,F$. The circuit is driven by a \sinusoidal voltage source with a frequency of $f = 50\,Hz$. What is the impedance of the circuit?

A. 10\,\Omega

Correct B. 20\,\Omega

C. 30\,\Omega

D. 40\,\Omega

Correct Answer: B

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Question 13

A gas is confined to a container with a volume of $V = 10^{-3}\,m^3$. The gas is heated from an initial temperature of $T_1 = 300\,K$ to a final temperature of $T_2 = 400\,K$. Assuming the gas is ideal and the process is isobaric, what is the final volume of the gas?

A. 10^{-3}\,m^3

Correct B. 2\times 10^{-3}\,m^3

C. 3\times 10^{-3}\,m^3

D. 4\times 10^{-3}\,m^3

Correct Answer: B

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Question 14

A simple harmonic oscillator has a mass of $m = 2\,kg$ and a spring cons\tant of $k = 100\,N/m$. The oscillator is displaced from its equilibrium position by a dis\tance of $x_0 = 0.1\,m$. What is the maximum kinetic energy of the oscillator?

A. 0.1\,J

Correct B. 0.5\,J

C. 1.0\,J

D. 2.0\,J

Correct Answer: B

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Question 15

A circuit consists of a resistor, an inductor, and a capacitor connected in series. The resistor has a resis\tance of $R = 10\,\Omega$, the inductor has an induc\tance of $L = 0.1\,H$, and the capacitor has a capaci\tance of $C = 10^{-6}\,F$. The circuit is driven by a \sinusoidal voltage source with a frequency of $f = 50\,Hz$. What is the phase angle of the circuit?

A. 0

Correct B. \frac{\pi}{4}

C. \frac{\pi}{2}

D. \frac{3\pi}{4}

Correct Answer: B

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Question 16

A thermodynamic system undergoes a process from an initial state (i) to a final state (f). The process is described by the equation $ Delta U = Q - W $, where ( Delta U ) is the change in internal energy, ( Q ) is the heat added to the system, and ( W ) is the work done by the system. If the system undergoes an isothermal expansion, what is the relationship between ( Q ) and ( W )?

A. Q = W

Correct B. Q = -W

C. Q = 0

D. W = 0

Correct Answer: B

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Question 17

A beam of light passes from air into a glass slab of re\fractive index $ mu = 1.5 $. If the angle of incidence is $ 30^{circ} $, what is the angle of re\fraction?

Correct A. 20^{circ}

B. 25^{circ}

C. 30^{circ}

D. 35^{circ}

Correct Answer: A

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Question 18

A radioactive sample undergoes a decay process with a half-life of ( 10 ) years. If the initial activity is ( 100 ) Bq, what is the activity after ( 20 ) years?

A. 50 Bq

B. 25 Bq

Correct C. 12.5 Bq

D. 6.25 Bq

Correct Answer: C

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Question 19

A particle of mass ( m ) is confined to a one-dimensional box of length ( L ). The energy levels of the particle are given by the equation $ E_n = \frac{n^2 h^2}{8mL^2} $. If the particle is in the ground state, what is the energy of the particle?

Correct A. $ \frac{h^2}{8mL^2} $

B. $ \frac{h^2}{4mL^2} $

C. $ \frac{h^2}{2mL^2} $

D. $ \frac{h^2}{mL^2} $

Correct Answer: A

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Question 20

A lens of focal length ( f ) is used to form an image of an object at a dis\tance ( u ) from the lens. The image dis\tance is given by the equation $ \frac{1}{v} = \frac{1}{f} + \frac{1}{u} $. If the object dis\tance is ( 20 ) cm and the focal length is ( 10 ) cm, what is the image dis\tance?

A. 30 cm

B. 40 cm

Correct C. 50 cm

D. 60 cm

Correct Answer: C

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Question 21

A 2.5 mH inductor is connected in series with a 10 Ω resistor and a 12 V battery. If the switch is closed at t = 0, what is the current in the circuit at t = 10 ms?

A. 0.5 A

Correct B. 1.0 A

C. 1.5 A

D. 2.0 A

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 cons\tant speed of 4 m/s. What is the magnitude of the force acting on the particle?

A. 8 N

B. 10 N

Correct C. 12 N

D. 15 N

Correct Answer: C

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Question 23

A 5 kg block is moving up a 30° incline with an initial speed of 2 m/s. If the coefficient of kinetic friction is 0.2, what is the acceleration of the block?

A. 0.5 m/s^2

Correct B. 1.0 m/s^2

C. 1.5 m/s^2

D. 2.0 m/s^2

Correct Answer: B

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Question 24

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

A. 20 Ω

B. 30 Ω

Correct C. 40 Ω

D. 50 Ω

Correct Answer: C

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Question 25

A 5 kg block is moving in a circular path of radius 2 m with a cons\tant speed of 3 m/s. What is the magnitude of the force acting on the block?

A. 6 N

B. 8 N

Correct C. 10 N

D. 12 N

Correct Answer: C

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