POST UTME UNIPORT 2024 Physics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A 2.5 m long wire of resis\tance 3.5 Ω is connected in series with a 4.2 V battery. If the wire is stretched to 3.2 m, what is the new resis\tance?
A. 2.1 Ω
B. 2.5 Ω
C. 3.1 Ω
D. 3.5 Ω
Question 2
A simple harmonic motion is described by the equation x(t) = 2\cos\( ωt + φ \). If the amplitude of the motion is 2 m, what is the value of φ?
A. 0°
B. 30°
C. 45°
D. 60°
Question 3
A particle of mass $m$ is moving in a circular orbit of radius $r$ under the influence of a central force given by $F(r) = \frac{k}{r^2}$. If the particle's angular momentum is $L = 2mvr$, find the total energy of the particle in terms of $k$, $m$, and $r$.
A. \( E = \frac{k}{2mr} \)
B. \( E = \frac{k}{mr} \)
C. \( E = \frac{1}{2}mv^2 + \frac{k}{r} \)
D. \( E = \frac{1}{2}mv^2 - \frac{k}{2r} \)
Question 4
A particle of mass $m$ is moving in a circular orbit of radius $r$ under the influence of a central force given by $F(r) = \frac{k}{r^2}$. If the particle's angular momentum is $L = 2mvr$, find the total energy of the particle in terms of $k$, $m$, and $r$.
A. \( E = \frac{k}{2mr} \)
B. \( E = \frac{k}{mr} \)
C. \( E = \frac{1}{2}mv^2 + \frac{k}{r} \)
D. \( E = \frac{1}{2}mv^2 - \frac{k}{2r} \)
Question 5
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\( \frac{npi x}{L}\right \)). What is the expectation value of the position operator for this particle?
A. \frac{L}{2}
B. \frac{L}{4}
C. \frac{3L}{4}
D. \frac{L}{3}
Question 6
A ray of light passes from air into a glass of re\fractive index 1.5. If the angle of incidence is 30°, find the angle of re\fraction.
A. 20°
B. 30°
C. 40°
D. 50°
Question 7
A beam of light passes from air into a block of glass. If the angle of incidence is 30°, what is the angle of re\fraction?
A. 20°
B. 25°
C. 30°
D. 35°
Question 8
A 5 kg block is moving down a 30° inclined plane with a cons\tant acceleration of 2 m/s². What is the force of friction acting on the block?
A. 10 N
B. 15 N
C. 20 N
D. 25 N
Question 9
A wave has a frequency of 50 Hz and a wavelength of 0.1 m. Find the speed of the wave.
A. 5 m/s
B. 10 m/s
C. 20 m/s
D. 50 m/s
Question 10
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 statements is true about the behavior of the gas?
A. The volume of the gas decreases.
B. The pressure of the gas increases.
C. The number of moles of the gas increases.
D. The gas expands to fill the container.
Question 11
A circuit consists of a 10 Ω resistor, a 20 Ω resistor, and a 5 Ω resistor connected in series. If a voltage of 12 V is applied across the circuit, what is the current flowing through the 5 Ω resistor?
A. 0.5 A
B. 1 A
C. 2 A
D. 3 A
Question 12
A particle is moving in a circular path with a cons\tant speed of 5 m/s. If the radius of the circle is 2 m, what is the magnitude of the acceleration of the particle?
A. 10 m/s²
B. 20 m/s²
C. 25 m/s²
D. 30 m/s²
Question 13
A block of mass 5 kg is attached to a horizontal spring with a force cons\tant of 100 N/m. If the block is displaced by 2 m from its equilibrium position and released, what is the maximum speed of the block?
A. 2 m/s
B. 4 m/s
C. 6 m/s
D. 8 m/s
Question 14
A particle of mass 0.5 kg is attached to a spring with a spring 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 maximum kinetic energy of the particle.
A. 0.5 J
B. 1.0 J
C. 1.5 J
D. 2.0 J
Question 15
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 centripetal acceleration?
A. 1.33 m/s^2
B. 2.67 m/s^2
C. 4 m/s^2
D. 6.67 m/s^2

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