POST UTME SUMMIT UNIVERSITY 2018 Physics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A point charge of +2 μC is placed 3 cm from a point charge of -3 μC. What is the magnitude of the electric field at the midpoint between the charges?
A. 1.5 × 10^4 N/C
B. 2.0 × 10^4 N/C
C. 2.5 × 10^4 N/C
D. 3.0 × 10^4 N/C
Question 2
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 speed is $v$, what is the total energy of the particle?
A. $\frac{1}{2}mv^2 + \frac{k}{r}$
B. $\frac{1}{2}mv^2 - \frac{k}{r}$
C. $\frac{1}{2}mv^2 + \frac{k}{r^2}$
D. $\frac{1}{2}mv^2 - \frac{k}{r^2}$
Question 3
A spring with spring cons\tant $k$ is stretched by a dis\tance $x$. What is the magnitude of the force exerted by the spring on the object attached to it?
A. \( kx \)
B. \( \frac{k}{x} \)
C. \( \frac{k}{x^2} \)
D. \( k^2x \)
Question 4
A particle of mass $m$ is attached to a spring with spring cons\tant $k$. If the particle is displaced by a dis\tance $x$ from its equilibrium position and released from rest, what is the equation of motion of the particle?
A. \( m\frac{d^2x}{dt^2} + kx = 0 \)
B. \( m\frac{d^2x}{dt^2} - kx = 0 \)
C. \( m\frac{d^2x}{dt^2} + \frac{k}{m}x = 0 \)
D. \( m\frac{d^2x}{dt^2} - \frac{k}{m}x = 0 \)
Question 5
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. \( \frac{mv^2}{r^2} \)
Question 6
A gas is heated from 300 K to 400 K at cons\tant volume. If the initial pressure is 2.0 atm, what is the final pressure?
A. 2.5 atm
B. 3.0 atm
C. 3.5 atm
D. 4.0 atm
Question 7
A quantum particle of mass $m$ is confined to a one-dimensional box of length $L$. What is the ground-state energy of the particle?
A. E_1 = \frac{h^2}{4mL^2}
B. E_1 = \frac{h^2}{8mL^2}
C. E_1 = \frac{h^2}{16mL^2}
D. E_1 = \frac{h^2}{32mL^2}
Question 8
A sound wave with a frequency of 200 Hz and a wavelength of 0.5 m is traveling through a medium with a speed of 340 m/s. What is the amplitude of the wave?
A. 0.1 m
B. 0.2 m
C. 0.3 m
D. 0.4 m
Question 9
A parallel plate capacitor has plates of area $A$ and separation $d$. If the capaci\tance is $C$, what is the value of the dielectric cons\tant $K$?
A. 1
B. 2
C. 3
D. 4
Question 10
A radioactive sample has an initial activity of 100 Bq. After 2 hours, the activity decreases to 50 Bq. What is the half-life of the sample?
A. 1 hour
B. 2 hours
C. 4 hours
D. 6 hours
Question 11
A circuit consists of a battery of emf $\mathcal{E}$, a resistor of resis\tance $R$, and an inductor of induc\tance $L$. If the circuit is connected to a switch that is closed at time $t=0$, what is the equation of the current in the circuit?
A. \( I(t) = \frac{\mathcal{E}}{R} \left\( 1 - e^{-\frac{Rt}{L}} \right \)
B. \( I(t) = \frac{\mathcal{E}}{R} \left\( 1 + e^{-\frac{Rt}{L}} \right \)
C. \( I(t) = \frac{\mathcal{E}}{R} \left\( 1 - e^{-\frac{Lt}{R}} \right \)
D. \( I(t) = \frac{\mathcal{E}}{R} \left\( 1 + e^{-\frac{Lt}{R}} \right \)
Question 12
A heat engine operates between a high-temperature reservoir at 500 K and a low-temperature reservoir at 300 K. If the engine produces 200 J of work per cycle, what is the efficiency of the engine?
A. 0.4
B. 0.5
C. 0.6
D. 0.7
Question 13
A block of mass $m$ is placed on a horizontal, frictionless surface. A force of magnitude $F$ is applied to the block, cau\sing it to accelerate at a rate $a$. What is the magnitude of the normal force exerted by the surface on the block?
A. \( mg \)
B. \( ma \)
C. \( F \)
D. \( mg + ma \)
Question 14
A block of mass 5 kg is placed on a frictionless surface and attached to a horizontal spring with a force cons\tant of 200 N/m. If the block is displaced by 0.2 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 15
A magnetic field of strength 0.5 T is directed perp\endicular to a current-carrying wire of length 2 m. If the current in the wire is 2 A, what is the magnitude of the force acting on the wire?
A. 0.5 N
B. 1 N
C. 1.5 N
D. 2 N

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