POST UTME IMS U 2021 Physics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A point charge $q$ is placed at the center of a spherical shell of radius $R$. If the shell is given a charge $Q$, what is the electric potential $V$ at the surface of the shell?
A. \frac{q}{4\pi \epsilon_0 R}
B. \frac{Q}{4\pi \epsilon_0 R}
C. \frac{q+Q}{4\pi \epsilon_0 R}
D. \frac{q-Q}{4\pi \epsilon_0 R}
Question 2
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. 25°
C. 30°
D. 35°
Question 3
A 10 μF capacitor is connected in series with a 5 kΩ resistor and a 20 V battery. If the switch is closed at time t = 0, what is the time cons\tant of the circuit?
A. 0.1 s
B. 0.5 s
C. 1 s
D. 2 s
Question 4
A particle of mass $m$ is in a one-dimensional potential well of depth $V_0$ and width $L$. If the particle is in the ground state, what is the energy $E_0$?
A. \frac{\hbar^2 \pi^2}{2mL^2}
B. \frac{\hbar^2 \pi^2}{mL^2}
C. \frac{\hbar^2}{2mL^2}
D. \frac{\hbar^2}{mL^2}
Question 5
A sound wave has a frequency of 200 Hz and a wavelength of 1.5 m. What is the speed of the sound wave?
A. 300 m/s
B. 400 m/s
C. 500 m/s
D. 600 m/s
Question 6
A magnetic field $B$ is directed perp\endicular to a current-carrying wire of length $L$. If the current is $I$, what is the force $F$ on the wire?
A. ILB
B. \frac{ILB}{L}
C. \frac{ILB}{L^2}
D. \frac{ILB^2}{L}
Question 7
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_0\( x \ \) = \sqrt{\frac{2}{L}} \sinleft\( \frac{pi x}{L}\right \)). What is the expectation value of the position operator for this state?
A. \frac{L}{2}
B. \frac{L}{4}
C. \frac{3L}{4}
D. \frac{L}{pi}
Question 8
A body is moving in a circular path with a radius of 2 m. If the body completes one revolution in 10 s, what is its angular velocity?
A. 0.2 rad/s
B. 0.5 rad/s
C. 1 rad/s
D. 2 rad/s
Question 9
A particle of mass 5kg is moving in a circular path with a radius of 2m. If the particle has a speed of 10m/s, what is the magnitude of the centripetal acceleration?
A. 5m/s^2
B. 10m/s^2
C. 15m/s^2
D. 20m/s^2
Question 10
A particle of mass $m$ is moving in a simple harmonic motion with a frequency $f$. If the amplitude of the motion is doubled to $2A$, what is the new maximum kinetic energy $K_{max,new}$?
A. \( \frac{1}{2}m\( 2A \ \)^2(2pi f)^2 )
B. \( \frac{1}{2}m\( 2A \ \)^2(2pi f)^2 )
C. \( \frac{1}{2}m\( 2A \ \)^2(2pi f)^2 )
D. \( \frac{1}{2}m\( 2A \ \)^2(2pi f)^2 )
Question 11
A body of mass 2 kg is moving with a velocity of 5 m/s. If the force applied to it is 10 N, what is the acceleration of the body?
A. 0.5 m/s²
B. 1 m/s²
C. 2 m/s²
D. 5 m/s²
Question 12
A ray of light passes through a prism and is re\fracted. If the angle of incidence is 30° and the angle of re\fraction is 20°, what is the angle of deviation?
A. 50°
B. 60°
C. 70°
D. 80°
Question 13
A wave has a frequency of 50 Hz and a wavelength of 0.1 m. What is its speed?
A. 5 m/s
B. 10 m/s
C. 20 m/s
D. 50 m/s
Question 14
A charged particle of mass $m$ and charge $q$ is moving in a uniform magnetic field $mathbf{B} = B_0 hat{mathbf{z}}$. If the particle has an initial velocity $mathbf{v} = v_0 hat{mathbf{x}}$, what is the radius of the circular orbit that the particle will follow?
A. \frac{mv_0}{qB_0}
B. \frac{qB_0}{mv_0}
C. \frac{mv_0^2}{qB_0}
D. \frac{qB_0^2}{m}
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. If the particle is subjected to a centripetal acceleration of 2 m/s^2, what is the magnitude of the force acting on the particle?
A. 12 N
B. 16 N
C. 20 N
D. 24 N

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