POST UTME AFE BABALOLA UNIVERSITY 2021 Physics | Objective

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Question 1
A uniform solid sphere of radius $R$ and mass $M$ is placed at the bottom of a deep well. The well is filled with a fluid of density $\rho$. If the sphere is displaced slightly from its equilibrium position, it will oscillate with a frequency given by the equation $f = \frac{1}{2pi}\sqrt{\frac{3pi^2\rho g}{2R}}$. What is the value of $f$ if $R = 0.1\text{ m}$, $M = 5\text{ kg}$, $\rho = 1000\text{ kg/m}^3$, and $g = 9.8\text{ m/s}^2$?
A. 0.5 Hz
B. 1.0 Hz
C. 1.5 Hz
D. 2.0 Hz
Question 2
A wave of frequency 100 Hz and wavelength 2 m is traveling through a medium. What is the speed of the wave?
A. 200 m/s
B. 400 m/s
C. 600 m/s
D. 800 m/s
Question 3
A ray of light passes from air into a glass of re\fractive index 1.5. If the angle of incidence is 30°, what is the angle of re\fraction?
A. 20°
B. 30°
C. 40°
D. 50°
Question 4
A particle of mass 1 kg is moving in a simple harmonic motion with a frequency of 5 Hz. If the amplitude of the motion is 2 m, what is the maximum acceleration of the particle?
A. 10 m/s^2
B. 20 m/s^2
C. 30 m/s^2
D. 40 m/s^2
Question 5
A body of mass 3 kg is moving in a circular path of radius 2 m with a cons\tant speed of 3 m/s. If the body is subjected to a centripetal force of 15 N, what is the work done by the centripetal force in moving the body through a dis\tance of 15 m?
A. 135 J
B. 150 J
C. 165 J
D. 180 J
Question 6
A beam of light is incident on a glass surface at an angle of 30°. If the re\fractive index of glass is 1.5, what is the angle of re\fraction?
A. 30°
B. 48.59°
C. 60°
D. 75°
Question 7
A body 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 body is subjected to a centripetal force of 12 N, what is the work done by the centripetal force in moving the body through a dis\tance of 10 m?
A. 60 J
B. 80 J
C. 100 J
D. 120 J
Question 8
A gas is contained in a cylinder of volume $V$ and is subjected to a pressure $P$. If the gas is heated, what is the change in the pressure of the gas?
A. \( \frac{P\Delta V}{V} \)
B. \( \frac{P\Delta V}{2V} \)
C. \( \frac{P\Delta V}{3V} \)
D. \( \frac{P\Delta V}{4V} \)
Question 9
A capacitor consists of two parallel plates, each of area $A$ and separation $d$. The capacitor is connected to a battery of emf $V$. If the dielectric cons\tant of the material between the plates is $K$, what is the capaci\tance of the capacitor?
A. \( \frac{KA\epsilon_0}{d} \)
B. \( \frac{KA\epsilon_0}{2d} \)
C. \( \frac{KA\epsilon_0}{3d} \)
D. \( \frac{KA\epsilon_0}{4d} \)
Question 10
A wave has a frequency of 100 Hz and a wavelength of 0.1 m. What is the speed of the wave?
A. 20 m/s
B. 30 m/s
C. 40 m/s
D. 50 m/s
Question 11
A circuit consists of a resistor of resis\tance $R$ and an inductor of induc\tance $L$ connected in series. The circuit is driven by a voltage source of voltage $V$. What is the impedance of the circuit?
A. R + ωL
B. R - ωL
C. √\( R^2 + \( ωL \ \)^2)
D. R√\( 1 + \( ωL \ \)^2)
Question 12
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. 0.6 A
B. 1.2 A
C. 2.4 A
D. 3.6 A
Question 13
A block of mass 5 kg is attached to a horizontal spring with a force cons\tant of 200 N/m. If the block is displaced by 0.1 m from its equilibrium position and released from rest, what is the maximum speed of the block?
A. 0.5 m/s
B. 1 m/s
C. 1.5 m/s
D. 2 m/s
Question 14
A particle of mass 1 kg is moving in a straight line with an initial velocity of 5 m/s. If the particle is subjected to a force of 10 N, what is the acceleration of the particle after 2 s?
A. 2 m/s^2
B. 4 m/s^2
C. 6 m/s^2
D. 8 m/s^2
Question 15
A light ray passes from air into a glass slab of re\fractive index 1.5. If the angle of incidence is 30°, what is the angle of re\fraction?
A. 20°
B. 30°
C. 40°
D. 50°

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