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POST UTME CHRISTOPHER UNIVERSITY 2023 Physics | Objective

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Question 1 View Details

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 of the particle?

Correct A. \frac{L}{2}

B. \frac{L}{4}

C. \frac{3L}{4}

D. \frac{L}{3}

Correct Answer: A

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Question 2 View Details

A parallel plate capacitor has a capaci\tance of $C = 2 \times 10^{-6} \, \text{F}$ and is charged to a potential difference of $V = 100 \, \text{V}$. The plates are then disconnected from the power source and the dis\tance between them is increased to $d = 5 \, \text{mm}$. What is the new potential difference across the plates?

A. 50 \, \text{V}

B. 75 \, \text{V}

C. 100 \, \text{V}

Correct D. 125 \, \text{V}

Correct Answer: D

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Question 3 View Details

A simple harmonic motion has a period of $T = 2 \, \text{s}$ and an amplitude of $A = 0.5 \, \text{m}$. What is the angular frequency of the motion?

A. 1.57 \, \text{rad/s}

B. 3.14 \, \text{rad/s}

Correct C. 6.28 \, \text{rad/s}

D. 10.47 \, \text{rad/s}

Correct Answer: C

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Question 4 View Details

A radioactive sample has a half-life of $T_{1/2} = 10 \, \text{min}$. If the initial activity of the sample is $A_0 = 100 \, \text{Bq}$, what is the activity of the sample after $t = 20 \, \text{min}$?

A. 12.5 \, \text{Bq}

Correct B. 25 \, \text{Bq}

C. 50 \, \text{Bq}

D. 100 \, \text{Bq}

Correct Answer: B

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Question 5 View Details

A sound wave has a frequency of $f = 200 \, \text{Hz}$ and a speed of $v = 343 \, \text{m/s}$. What is the wavelength of the sound wave?

A. 1.71 \, \text{m}

Correct B. 2.86 \, \text{m}

C. 4.29 \, \text{m}

D. 5.71 \, \text{m}

Correct Answer: B

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Question 6 View Details

A particle of mass 2 kg is attached to a spring with a force cons\tant of 100 N/m. The particle is displaced by 0.2 m from its equilibrium position and released from rest. Assuming the motion is simple harmonic, calculate the angular frequency of the particle's motion.

A. 10 rad/s

B. 5 rad/s

Correct C. 20 rad/s

D. 15 rad/s

Correct Answer: C

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Question 7 View Details

A heat engine operates between two reservoirs at temperatures 500 K and 300 K. The engine receives 1000 J of heat from the high-temperature reservoir and rejects 600 J of heat to the low-temperature reservoir. Calculate the efficiency of the engine.

A. 0.4

Correct B. 0.5

C. 0.6

D. 0.7

Correct Answer: B

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Question 8 View Details

A wave with a frequency of 20 Hz and a wavelength of 0.5 m is traveling through a medium. Calculate the speed of the wave.

A. 10 m/s

Correct B. 20 m/s

C. 30 m/s

D. 40 m/s

Correct Answer: B

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Question 9 View Details

A capacitor consists of two parallel plates, each with an area of 0.01 m^2 and separated by a dis\tance of 0.001 m. The plates are charged to a potential difference of 10 V. Calculate the capaci\tance of the capacitor.

Correct A. 10^-9 F

B. 10^-10 F

C. 10^-11 F

D. 10^-12 F

Correct Answer: A

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Question 10 View Details

A magnetic field of 0.5 T is directed perp\endicular to the plane of a circular loop of wire with a radius of 0.1 m. Calculate the magnetic flux through the loop.

Correct A. 5\times 10^{-4} Wb

B. 10^{-4} Wb

C. 5\times 10^{-5} Wb

D. 10^{-5} Wb

Correct Answer: A

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Question 11 View Details

A 1000 W heater is used to heat water in a thermos flask. If the heater operates at 90% efficiency, calculate the rate of heat transfer from the heater to the water.

Correct A. 900 W

B. 1000 W

C. 1100 W

D. 1200 W

Correct Answer: A

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Question 12 View Details

A 200 V, 50 Hz AC supply is connected to a resistor of 10 Ω. Calculate the rms value of the current flowing through the resistor.

A. 2 A

Correct B. 4 A

C. 6 A

D. 8 A

Correct Answer: B

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Question 13 View Details

A body of mass 2 kg is moving in a circular path with a radius of 3 m. If the body is moving at a speed of 4 m/s, calculate the centripetal acceleration of the body.

A. 0.5 m/s^2

B. 1 m/s^2

Correct C. 2 m/s^2

D. 4 m/s^2

Correct Answer: C

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Question 14 View Details

A radioactive sample has a half-life of 5 years. If the initial activity of the sample is 100 Bq, calculate the activity of the sample after 10 years.

Correct A. 12.5 Bq

B. 25 Bq

C. 50 Bq

D. 100 Bq

Correct Answer: A

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Question 15 View Details

A simple harmonic motion has a maximum displacement of 2 m and a frequency of 3 Hz. Calculate the angular frequency of the motion.

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 16 View Details

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 acceleration of 2 m/s^2, what is the magnitude of the net force acting on the particle?

A. 8 N

Correct B. 10 N

C. 12 N

D. 16 N

Correct Answer: B

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Question 17 View Details

A heat engine operates between the temperatures of 500 K and 300 K. If the engine has an efficiency of 30%, what is the maximum possible work output?

A. 1000 J

B. 1500 J

Correct C. 2000 J

D. 2500 J

Correct Answer: C

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Question 18 View Details

A capacitor consists of two parallel plates, each with a surface area of 0.1 m^2. The dis\tance between the plates is 0.01 m. If the capaci\tance is 10 nF, what is the charge stored on the capacitor when a potential difference of 5 V is applied?

A. 50 nC

Correct B. 100 nC

C. 150 nC

D. 200 nC

Correct Answer: B

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Question 19 View Details

A gas expands from an initial volume of 0.1 m^3 to a final volume of 0.5 m^3 at a cons\tant temperature of 300 K. If the initial pressure is 100 kPa, what is the final pressure?

A. 20 kPa

B. 30 kPa

Correct C. 40 kPa

D. 50 kPa

Correct Answer: C

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Question 20 View Details

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?

A. 10 m

B. 15 m

Correct C. 20 m

D. 25 m

Correct Answer: C

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