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POST UTME LEAD CITY UNIVERSITY 2023 Physics | Objective

Are you preparing for POST UTME LEAD CITY UNIVERSITY 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.

Practice these randomly selected questions to test your readiness.

Question 1

A particle of mass $m$ is confined to a one-dimensional box of length $L$. The wave function of the particle is given by $psi(x) = \sqrt{\frac{2}{L}} \sinleft$ \frac{npi x}{L}\right $$, where $n$ is a positive integer. What is the expectation value of the position of the particle in the ground state $ $n=1$ $?

A. 0

Correct B. L/2

C. L

D. L/4

Correct Answer: B

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Question 2

A capacitor consists of two parallel plates, each of area $A$, separated by a dis\tance $d$. The plates are charged to a potential difference $V$. What is the capaci\tance of the capacitor?

Correct A. \frac{\epsilon_0 A}{d}

B. \frac{\epsilon_0 A}{2d}

C. \frac{2\epsilon_0 A}{d}

D. \frac{\epsilon_0 A}{2d^2}

Correct Answer: A

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Question 3

A heat engine operates between two temperatures $T_1$ and $T_2$, where $T_1 > T_2$. The engine has an efficiency of $\eta = 1 - \frac{T_2}{T_1}$. What is the maximum possible efficiency of the engine?

Correct A. 1 - \frac{T_2}{T_1}

B. 1 - \frac{T_1}{T_2}

C. \frac{T_1 - T_2}{T_1}

D. \frac{T_2 - T_1}{T_2}

Correct Answer: A

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Question 4

A particle of mass $m$ is moving in a circular orbit of radius $r$ with a speed $v$. The particle is subject to a centripetal force $F_c = \frac{mv^2}{r}$. What is the kinetic energy of the particle?

Correct A. \frac{1}{2}mv^2

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

C. \frac{1}{2}mvr

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

Correct Answer: A

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Question 5

A radioactive sample decays at a rate given by the equation $\frac{dN}{dt} = -\lambda N$, where $N$ is the number of nuclei and $\lambda$ is the decay cons\tant. What is the half-life of the sample?

Correct A. \frac{\ln 2}{\lambda}

B. \frac{\lambda}{\ln 2}

C. \frac{1}{\lambda}

D. \frac{\lambda}{2}

Correct Answer: A

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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 force?

A. 10 N

Correct B. 12 N

C. 15 N

D. 20 N

Correct Answer: B

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Question 7

A charged particle of mass 1.5 kg and charge 3 C is moving in a magnetic field of strength 2 T. If the particle is moving with a speed of 5 m/s, what is the magnitude of the force acting on the particle?

A. 0.15 N

B. 0.30 N

Correct C. 0.45 N

D. 0.60 N

Correct Answer: C

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Question 8

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/s², 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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Question 9

A 10 Ω resistor and a 20 Ω resistor are connected in series. If a voltage of 12 V is applied across the circuit, what is the current flowing through the circuit?

A. 0.4 A

B. 0.6 A

Correct C. 0.8 A

D. 1.0 A

Correct Answer: C

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Question 10

A 5 kg block is moving with a velocity of 2 m/s on a frictionless surface. If a force of 10 N is applied to the block, what is the acceleration of the block?

A. 0.5 m/s²

B. 1.0 m/s²

Correct C. 1.5 m/s²

D. 2.0 m/s²

Correct Answer: C

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Question 11

A particle of mass $m$ is attached to a spring with spring cons\tant $k$. If the particle is displaced by a dis\tance $x$ from its equilibrium position and released from rest, it will execute simple harmonic motion with angular frequency $omega$. Which of the following expressions for $omega$ is correct?

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

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

C. \omega = \frac{1}{\sqrt{mk}}

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

Correct Answer: D

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Question 12

A radioactive sample has a half-life of $t_{1/2}$. If the initial activity of the sample is $A_0$, what is the activity of the sample after a time $t$?

Correct A. A_0 \left$ \frac{1}{2}\right $^{t/t_{1/2}}

B. A_0 \left$ \frac{1}{2}\right $^{t_{1/2}/t}

C. A_0 \left$ \frac{1}{2}\right $^{t/t_{1/2}} + A_0

D. A_0 \left$ \frac{1}{2}\right $^{t/t_{1/2}} - A_0

Correct Answer: A

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Question 13

A wave has a frequency of $f$ and a wavelength of $\lambda$. What is the speed of the wave?

A. f \lambda

Correct B. \frac{f}{\lambda}

C. \frac{\lambda}{f}

D. f^2 \lambda^2

Correct Answer: B

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Question 14

A magnetic field is produced by a current-carrying wire. If the current is increased by a factor of $n$, what happens to the magnetic field?

Correct A. Increases by a factor of $n$

B. Decreases by a factor of $n$

C. Increases by a factor of $n^2$

D. Decreases by a factor of $n^2$

Correct Answer: A

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Question 15

A sound wave has a frequency of $f$ and a speed of $v$. What is the wavelength of the wave?

Correct A. \frac{v}{f}

B. \frac{f}{v}

C. \frac{v^2}{f}

D. \frac{f^2}{v}

Correct Answer: A

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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. 0.5 A

B. 1 A

Correct C. 2 A

D. 5 A

Correct Answer: C

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Question 18

A projectile is launched from the ground with an initial velocity of 20 m/s at an angle of 30° 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

Correct B. 20 m

C. 30 m

D. 40 m

Correct Answer: B

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Question 19

A circuit consists of a 10 Ω resistor and a 20 μF capacitor connected in series. If a voltage of 100 V is applied across the circuit, what is the time cons\tant of the circuit?

A. 0.2 s

B. 0.5 s

Correct C. 1 s

D. 2 s

Correct Answer: C

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Question 20

A 100 W light bulb is connected to a 220 V power source. If the resis\tance of the light bulb is 50 Ω, what is the current flowing through the light bulb?

A. 0.5 A

Correct B. 1 A

C. 2 A

D. 5 A

Correct Answer: B

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Question 21

A uniform solid sphere of radius R and mass M is placed in a container filled with a fluid of density ρ. The sphere is partially submerged in the fluid, with a volume V submerged. What is the pressure at the bottom of the sphere?

A. ρgV

Correct B. ρg$ R^3 - V $

C. ρg$ R^3 - V $/V

D. ρg$ R^3 - V $/R

Correct Answer: B

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Question 22

A gas is compressed from an initial volume of 2.0 m^3 to a final volume of 1.0 m^3 at a cons\tant temperature of 300 K. What is the work done on the gas?

A. 2000 J

Correct B. 4000 J

C. 6000 J

D. 8000 J

Correct Answer: B

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Question 23

A coil of wire with 100 turns is placed in a magnetic field of 0.5 T. The coil has a radius of 0.05 m and a length of 0.1 m. What is the magnetic flux through the coil?

A. 0.01 Wb

Correct B. 0.02 Wb

C. 0.03 Wb

D. 0.04 Wb

Correct Answer: B

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Question 24

A particle of mass 0.5 kg is moving in a circular path with a radius of 0.2 m. The particle has a speed of 2.0 m/s. What is the centripetal acceleration of the particle?

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 25

A simple harmonic motion has a maximum displacement of 0.5 m and a period of 2.0 s. What is the angular frequency of the motion?

A. 0.5 rad/s

Correct B. 1.0 rad/s

C. 1.5 rad/s

D. 2.0 rad/s

Correct Answer: B

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