POST UTME PAN-ATLANTIC UNIVERSITY 2023 Physics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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, what is its potential energy $U$?
A. \( U = \frac{1}{2} kx^2 \)
B. \( U = kx^2 \)
C. \( U = \frac{1}{2} kx \)
D. \( U = kx \)
Question 2
A particle of mass 0.1 kg is attached to a spring with a force cons\tant of 10 N/m. The particle is displaced by 0.1 m from its equilibrium position and released from rest. Assuming the particle undergoes simple harmonic motion, calculate the time period of the motion.
A. 0.1 s
B. 0.2 s
C. 0.3 s
D. 0.4 s
Question 3
A gas occupies a volume of 2.5 L at a pressure of 1.5 atm. If the pressure is increased to 3 atm, what is the new volume of the gas?
A. 1 L
B. 1.25 L
C. 1.5 L
D. 1.75 L
Question 4
A 100 W light bulb is connected to a 230 V power source. If the bulb is used for 5 hours a day, calculate the total energy consumed in a month (30 days).
A. 900 kWh
B. 1000 kWh
C. 1100 kWh
D. 1200 kWh
Question 5
A 100 V, 50 Hz AC supply is connected to a circuit containing a 50 Ω resistor and a 20 μF capacitor in series. Calculate the impedance of the circuit.
A. 50 Ω
B. 60 Ω
C. 70 Ω
D. 80 Ω
Question 6
A wave function is given by ψ(x) = Ae^\( -αx^2 \). If the wave function is normalized, what is the value of A?
A. 1/√(2α)
B. 1/√(α)
C. √(α)
D. α
Question 7
A particle of mass 0.5 kg is moving in a circular path of radius 2 m with a cons\tant speed of 4 m/s. What is the magnitude of the force acting on the particle?
A. 2 N
B. 4 N
C. 6 N
D. 8 N
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 air resis\tance is neglected, calculate the maximum height reached.
A. 10.0 m
B. 20.0 m
C. 30.0 m
D. 40.0 m
Question 9
A gas is enclosed in a container with a movable piston. The gas is heated, cau\sing its temperature to increase. Which of the following best describes the change in the gas's pressure?
A. The pressure remains cons\tant.
B. The pressure increases exponentially.
C. The pressure increases linearly with temperature.
D. The pressure decreases as the gas expands.
Question 10
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. Assuming the block undergoes simple harmonic motion, calculate the maximum speed of the block.
A. 0.5 m/s
B. 1.0 m/s
C. 1.5 m/s
D. 2.0 m/s
Question 11
A particle of mass 1 kg is moving in a straight line with a velocity of 5 m/s. If a force of 10 N is applied to the particle, what is the acceleration?
A. 2 m/s^2
B. 4 m/s^2
C. 6 m/s^2
D. 8 m/s^2
Question 12
A heat engine operates between two temperatures $T_1 = 500 K$ and $T_2 = 300 K$. If the engine produces 500 J of work, what is its efficiency $\eta$?
A. \( \eta = \frac{W}{Q_1} \)
B. \( \eta = \frac{Q_1 - W}{Q_1} \)
C. \( \eta = \frac{Q_1}{Q_1 - W} \)
D. \( \eta = \frac{W}{Q_1 - W} \)
Question 13
A block of wood is floating in water. If the block has a volume of 0.5 m^3 and a density of 500 kg/m^3, what is the buoyant force acting on the block?
A. 250 N
B. 500 N
C. 750 N
D. 1000 N
Question 14
A 10 μC charge is placed at the center of a hollow, conducting sphere of radius 0.1 m. Calculate the electric field at a dis\tance of 0.05 m from the center of the sphere.
A. 10^4 N/C
B. 10^5 N/C
C. 10^6 N/C
D. 10^7 N/C
Question 15
A projectile is launched from the ground with an initial velocity of 20 m/s at an angle of 60° above the horizontal. What is the maximum height reached by the projectile?
A. 10 m
B. 15 m
C. 20 m
D. 25 m

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