POST UTME IMS U 2021 Physics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A parallel plate capacitor has a capaci\tance of 2 μF and is charged to a potential difference of 10 V. If a dielectric slab of thickness 2 mm and dielectric cons\tant 3 is inserted between the plates, what is the new capaci\tance?
A. 4 μF
B. 6 μF
C. 8 μF
D. 10 μF
Question 2
A capacitor consists of two parallel plates, each of area 0.1m^2, separated by a dis\tance of 0.01m. If the capaci\tance is 10nF, what is the charge stored on the capacitor when a potential difference of 5V is applied across it?
A. 50nC
B. 100nC
C. 150nC
D. 200nC
Question 3
A 20 μF capacitor is connected in parallel with a 10 kΩ resistor and a 30 V battery. If the switch is closed at time t = 0, what is the time cons\tant of the circuit?
A. 0.2 s
B. 0.5 s
C. 1 s
D. 2 s
Question 4
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 5
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 6
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 7
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 $V$. If the area of the plates is doubled to $2A$, what is the new capaci\tance $C_{new}$?
A. \( \frac{epsilon_0 \( 2A \ \)}{d} )
B. \( \frac{epsilon_0 A}{2d} \)
C. \( \frac{epsilon_0 A}{d} \)
D. \( \frac{epsilon_0 A}{4d} \)
Question 8
A block of mass $M$ is attached to a horizontal spring with spring cons\tant $k$. The block is displaced by a dis\tance $x_0$ from its equilibrium position and released from rest. What is the angular frequency of the resulting simple harmonic motion?
A. \sqrt{\frac{k}{M}}
B. \frac{k}{M}
C. \frac{M}{k}
D. \sqrt{\frac{M}{k}}
Question 9
A radioactive sample has an initial activity of 100 Bq. If the half-life of the sample is 2 hours, what is the activity after 4 hours?
A. 50 Bq
B. 25 Bq
C. 12.5 Bq
D. 6.25 Bq
Question 10
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 11
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 12
A particle of mass $m$ is moving in a circular path of radius $R$ with a cons\tant speed $v$. The particle is subject to a centripetal force $F_c$ given by $F_c = \frac{mv^2}{R}$. If the particle's speed is doubled to $2v$, what is the new centripetal force $F_{c,new}$?
A. \( \frac{2mv^2}{R} \)
B. \( \frac{mv^2}{2R} \)
C. \( \frac{mv^2}{R} \)
D. \( \frac{4mv^2}{R} \)
Question 13
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 14
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
Question 15
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

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