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POST UTME MADONNA UNIVERSITY 2022 Physics | Objective

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Question 1

A 2.5 kg block of wood is attached to a horizontal, massless spring with a force cons\tant of 100 N/m. The block is displaced by 0.15 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 its equilibrium position.

A. 0.5 m/s

Correct B. 1.0 m/s

C. 1.5 m/s

D. 2.0 m/s

Correct Answer: B

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Question 2

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

A. 20°

B. 30°

Correct C. 40°

D. 50°

Correct Answer: C

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Question 3

A 10 μCi sample of radon-222 decays according to the first-order kinetics equation. If the half-life of radon-222 is 3.8 days, calculate the activity of the sample after 10 days.

A. 5 μCi

Correct B. 7.5 μCi

C. 10 μCi

D. 12.5 μCi

Correct Answer: B

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Question 4

A 50 Hz AC generator produces an emf of 100 V. If the generator is connected to a 10 Ω resistor, calculate the current flowing through the resistor.

A. 5 A

Correct B. 10 A

C. 15 A

D. 20 A

Correct Answer: B

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Question 5

A 2 kg block is attached to a horizontal, massless string with a length of 1.5 m. If the block is displaced by 0.2 m from its equilibrium position and released from rest, calculate the angular frequency of the block.

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 6

A 50 Hz, 200 V AC supply is connected to a 100 Ω resistor. Calculate the rms value of the current flowing through the resistor.

Correct A. 1.41 A

B. 1.41 mA

C. 14.1 A

D. 14.1 mA

Correct Answer: A

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Question 7

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. 32 N

Correct C. 48 N

D. 64 N

Correct Answer: C

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Question 8

A 2 kg block 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. Calculate the maximum speed of the block.

A. 2 m/s

B. 4 m/s

Correct C. 6 m/s

D. 8 m/s

Correct Answer: C

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Question 9

A 50 Hz, 200 V AC supply is connected to a 100 Ω resistor. Calculate the power consumed by the resistor.

A. 200 W

Correct B. 400 W

C. 600 W

D. 800 W

Correct Answer: B

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Question 10

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 centripetal acceleration.

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 11

A gas is heated from 300 K to 400 K at cons\tant volume. If the initial pressure is 1.5 atm, what is the final pressure?

Correct A. 2.25 atm

B. 1.5 atm

C. 3 atm

D. 4 atm

Correct Answer: A

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Question 12

A particle moves in a straight line with an initial velocity of 5 m/s. After 2 seconds, its velocity is 3 m/s. What is its acceleration?

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 13

A circuit consists of a 12 V battery, a 4 Ω resistor, and a 6 Ω resistor connected in series. What is the current flowing through the circuit?

A. 1 A

Correct B. 2 A

C. 3 A

D. 4 A

Correct Answer: B

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Question 14

A radioactive sample decays from 100 mg to 50 mg in 5 minutes. What is its half-life?

A. 2.5 minutes

Correct B. 5 minutes

C. 10 minutes

D. 15 minutes

Correct Answer: B

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Question 15

A projectile is launched at an angle of 30° to the horizontal with an initial velocity of 20 m/s. What is its range?

A. 40 m

B. 50 m

Correct C. 60 m

D. 70 m

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?

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 17

A capacitor of capaci\tance 10 μF is connected in series with a resistor of resis\tance 20 Ω. If a voltage of 50 V is applied across the circuit, what is the current flowing through the circuit?

A. 1.25 A

Correct B. 2.5 A

C. 5 A

D. 10 A

Correct Answer: B

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Question 18

A radioactive sample decays at a rate of 5% per hour. If the initial activity of the sample is 100 Bq, what is the activity of the sample after 2 hours?

A. 50 Bq

Correct B. 86.5 Bq

C. 100 Bq

D. 150 Bq

Correct Answer: B

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Question 19

A simple harmonic motion has a maximum displacement of 5 m and a frequency of 2 Hz. If the amplitude of the motion is 3 m, what is the angular frequency of the motion?

A. 10.2 rad/s

Correct B. 12.57 rad/s

C. 15.1 rad/s

D. 18.5 rad/s

Correct Answer: B

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Question 20

A circuit consists of a resistor of resis\tance 10 Ω and an inductor of induc\tance 5 H. If a voltage of 20 V is applied across the circuit, what is the current flowing through the circuit?

A. 1 A

Correct B. 1.33 A

C. 2 A

D. 3 A

Correct Answer: B

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Question 21

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 probability of finding the particle in the region $0 < x < \frac{L}{4}$?

Correct A. $ \frac{1}{8} $

B. $ \frac{1}{4} $

C. $ \frac{1}{2} $

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

Correct Answer: A

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Question 22

A sound wave with frequency $f$ is traveling through a medium with speed $v$. If the amplitude of the wave is doubled, what happens to the intensity of the wave?

A. The intensity remains the same.

B. The intensity increases by a factor of 2.

Correct C. The intensity increases by a factor of 4.

D. The intensity increases by a factor of 8.

Correct Answer: C

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Question 23

A gas is confined to a container with volume $V$. The gas is heated, cau\sing its temperature to increase by $Delta T$. What is the change in the pressure of the gas?

Correct A. (P Delta T)

B. (P Delta V)

C. (P Delta n)

D. (P Delta mu)

Correct Answer: A

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Question 24

A beam of light is incident on a surface with a re\fractive index $n_1$. The angle of incidence is $\theta_1$. What is the angle of re\fraction?

Correct A. $ \sin^{-1} left\( \frac{n_1}{n_2} \sin \theta_1 \right \ $ )

B. $ \sin^{-1} left\( \frac{n_2}{n_1} \sin \theta_1 \right \ $ )

C. $ \sin^{-1} left\( \frac{n_2}{n_1} \cos \theta_1 \right \ $ )

D. $ \sin^{-1} left\( \frac{n_1}{n_2} \cos \theta_1 \right \ $ )

Correct Answer: A

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Question 25

A lens with focal length $f$ is used to form an image of an object at a dis\tance $d$. What is the magnification of the lens?

Correct A. $ \frac{d}{f} $

B. $ \frac{f}{d} $

C. $ \frac{d - f}{f} $

D. $ \frac{f - d}{f} $

Correct Answer: A

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