POST UTME ABU 2018 Physics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A force $F$ is applied to a spring with spring cons\tant $k$. If the spring is displaced by a dis\tance $x$, what is the potential energy stored in the spring?
A. \frac{1}{2}kx^2
B. \frac{1}{2}Fx
C. \frac{1}{2}kx
D. \frac{1}{2}Fx^2
Question 2
A circuit consists of a resistor $R$, an inductor $L$, and a capacitor $C$ connected in series. If the circuit is driven by an AC voltage source with frequency $f$, what is the impedance $Z$ of the circuit?
A. \sqrt{R^2 + \( \omega L - 1/\omega C \)^2}
B. \sqrt{R^2 + \( \omega L + 1/\omega C \)^2}
C. \sqrt{R^2 + \( \omega L - 1/\omega C \)^2}
D. \sqrt{R^2 + \( \omega L + 1/\omega C \)^2}
Question 3
A circuit consists of a battery of emf $\mathcal{E} = 12 \text{V}$, a resistor of resis\tance $R = 2 \Omega$, and a capacitor of capaci\tance $C = 1 \mu\text{F}$. If the circuit is closed at time $t = 0$, what is the charge on the capacitor at time $t = 1 \text{s}$?
A. 0.5 \mu\text{C}
B. 1.0 \mu\text{C}
C. 1.5 \mu\text{C}
D. 2.0 \mu\text{C}
Question 4
A wave has a frequency of 50 Hz and a wavelength of 2 m. If the wave is traveling in the positive x-direction, what is the direction of the wave's velocity?
A. \( vec{v} = \frac{omega}{k} hat{i} \)
B. \( vec{v} = \frac{omega}{k} hat{j} \)
C. \( vec{v} = \frac{k}{omega} hat{i} \)
D. \( vec{v} = \frac{k}{omega} hat{j} \)
Question 5
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 force of 12 N, what is the magnitude of the acceleration of the particle?
A. 6 m/s^2
B. 12 m/s^2
C. 18 m/s^2
D. 24 m/s^2
Question 6
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 force of 12 N, what is the angular velocity of the particle?
A. 2 rad/s
B. 4 rad/s
C. 6 rad/s
D. 8 rad/s
Question 7
A circuit consists of a 12 V battery, a 4 Ω resistor, and a 6 Ω resistor connected in series. Calculate the total resis\tance of the circuit.
A. 10 Ω
B. 12 Ω
C. 14 Ω
D. 16 Ω
Question 8
A wave of frequency $f$ and amplitude $A$ is traveling through a medium with speed $v$. If the wave is reflected off a fixed \end, what is the amplitude of the reflected wave?
A. A
B. 2A
C. A/2
D. A/3
Question 9
A particle of mass $m$ is moving in a circular path of radius $r$ with a cons\tant speed $v$. If the particle is subjected to a uniform magnetic field of strength $B$, what is the magnitude of the magnetic force acting on the particle?
A. \( \frac{mv^2}{r} \)
B. \( \frac{mv}{r} \)
C. \( \frac{m^2v^2}{r^2} \)
D. \( \frac{mv^3}{r^2} \)
Question 10
A light ray passes through a prism of angle 30° and is re\fracted at an angle of 20°. What is the angle of deviation?
A. 10°
B. 20°
C. 30°
D. 40°
Question 11
A ray of light passes from air into a glass slab of re\fractive index $n = 1.5$. If the angle of incidence is $\theta_i = 30^\circ$, what is the angle of re\fraction $\theta_r$?
A. 20^\circ
B. 30^\circ
C. 40^\circ
D. 50^\circ
Question 12
A block of mass 5 kg is placed on a frictionless surface and attached to a horizontal spring with a force cons\tant of 20 N/m. If the block is displaced by 2 m from its equilibrium position and released from rest, 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 13
A heat engine operates between 300 K and 400 K. If the efficiency is 30%, what is the temperature of the hot reservoir?
A. 350 K
B. 400 K
C. 450 K
D. 500 K
Question 14
A charged particle of mass 1 kg and charge 2 C is moving in a uniform magnetic field of strength 3 T. If the particle has a velocity of 4 m/s, what is the magnitude of the force acting on the particle?
A. 12 N
B. 24 N
C. 36 N
D. 48 N
Question 15
A light source is placed 2 m away from a convex lens of focal length 1 m. If the light source is moved 1 m closer to the lens, what is the new image dis\tance?
A. 0.5 m
B. 1 m
C. 2 m
D. 3 m

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