POST UTME RSU 2018 Physics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A light wave with a frequency of 5 x 10^14 Hz is incident on a double-slit apparatus. The dis\tance between the slits is 0.5 mm. What is the wavelength of the light?
A. 500 nm
B. 1000 nm
C. 1500 nm
D. 2000 nm
Question 2
A parallel plate capacitor has a capaci\tance of 10 μF. If a potential difference of 20 V is applied across the plates, calculate the charge stored on the capacitor.
A. 200 μC
B. 400 μC
C. 600 μC
D. 800 μC
Question 3
A magnetic field of magnitude 0.5 T is directed perp\endicular to the plane of a circular loop of radius 0.1 m. If the loop carries a current of 2 A, calculate the torque experienced by the loop.
A. 0.01 Nm
B. 0.02 Nm
C. 0.03 Nm
D. 0.04 Nm
Question 4
A magnetic field is produced by a current-carrying wire. If the current is doubled, what happens to the magnetic field?
A. The magnetic field remains the same
B. The magnetic field increases by a factor of 2
C. The magnetic field increases by a factor of 4
D. The magnetic field decreases by a factor of 2
Question 5
A gas is enclosed in a container with a movable piston. The gas is heated, cau\sing its pressure to increase. Which of the following best describes the change in the gas's kinetic energy?
A. The gas's kinetic energy increases due to the increase in temperature.
B. The gas's kinetic energy remains cons\tant because the pressure increase is due to the piston's movement.
C. The gas's kinetic energy decreases due to the decrease in volume.
D. The gas's kinetic energy increases due to the increase in pressure.
Question 6
A sound wave has a frequency of 200 Hz and a wavelength of 1.5 m. Calculate the speed of the sound wave.
A. ( 300 ) m/s
B. ( 400 ) m/s
C. ( 500 ) m/s
D. ( 600 ) m/s
Question 7
A quantum particle is confined to a one-dimensional box of length 1 m. What is the ground-state energy of the particle?
A. 1.5 x 10^-34 J
B. 3.0 x 10^-34 J
C. 4.5 x 10^-34 J
D. 6.0 x 10^-34 J
Question 8
A block of mass 10 kg is placed on a frictionless surface. If a force of 30 N is applied to the block, calculate the acceleration produced in the block.
A. 3 m/s^2
B. 4 m/s^2
C. 5 m/s^2
D. 6 m/s^2
Question 9
A spring has a spring cons\tant of 100 N/m. If it is stretched by 2 m, calculate the work done in stretching the spring.
A. 200 J
B. 400 J
C. 600 J
D. 800 J
Question 10
A parallel plate capacitor has a capaci\tance of 10 μF. If a potential difference of 12 V is applied across the plates, calculate the charge stored on the capacitor.
A. 0.12 C
B. 0.24 C
C. 0.36 C
D. 0.48 C
Question 11
A 1000 W heater is used to heat a 5 kg block of copper from 20°C to 80°C. Calculate the time taken to heat the block u\sing the formula Q = mcΔT.
A. 10 s
B. 20 s
C. 30 s
D. 40 s
Question 12
A parallel plate capacitor has plates of area $A$ and separation $d$. The capaci\tance is given by $C = \frac{epsilon_0 A}{d}$. If the area is doubled and the separation is halved, what is the new capaci\tance?
A. $\frac{\epsilon_0 A}{d}$
B. $\frac{2\epsilon_0 A}{d}$
C. $\frac{\epsilon_0 A}{2d}$
D. $\frac{4\epsilon_0 A}{d}$
Question 13
A heat engine operates between two reservoirs at temperatures 500 K and 300 K. If the engine absorbs 100 J of heat from the high-temperature reservoir, calculate the efficiency of the engine.
A. 0.25
B. 0.30
C. 0.35
D. 0.40
Question 14
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_1\( x \ \) = \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 15
A vector $mathbf{a}$ has a magnitude of $5$ and makes an angle of $60^\circ$ with the positive $x$-axis. If a vector $mathbf{b}$ has a magnitude of $3$ and makes an angle of $30^\circ$ with the positive $y$-axis, what is the magnitude of the sum of the two vectors?
A. $4$
B. $5$
C. $6$
D. $7$

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