POST UTME OSUSTECH 2022 Physics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A simple harmonic motion has a maximum displacement of 10 cm and a time period of 2 s. If the motion starts from its mean position, what is the equation of motion?
A. x(t) = 10 \sin \( \pi t \)
B. x(t) = 10 \sin \( 2 \pi t \)
C. x(t) = 10 \sin \( \pi t + \frac{\pi}{2} \)
D. x(t) = 10 \sin \( 2 \pi t + \frac{\pi}{2} \)
Question 2
A ray of light passes through a prism and is re\fracted. If the angle of incidence is $30^circ$ and the angle of re\fraction is $45^circ$, what is the angle of deviation?
A. \( 60^circ \)
B. \( 45^circ \)
C. \( 30^circ \)
D. \( 20^circ \)
Question 3
A particle of mass $m$ is attached to a spring with spring cons\tant $k$. If the particle is displaced by a dis\tance $x$ and released from rest, what is the equation of motion?
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 4
A circuit consists of a resistor $R$, an inductor $L$, and a capacitor $C$ connected in series. The circuit is driven by a \sinusoidal voltage source with amplitude $V_0$ and frequency $f$. Find the impedance $Z$ of the circuit in terms of $R$, $L$, $C$, $V_0$, and $f$.
A. R + jωL - 1/jωC
B. R + jωL + 1/jωC
C. R - jωL + 1/jωC
D. R - jωL - 1/jωC
Question 5
A capacitor of 100 μF is connected across a 200 V DC supply. Calculate the energy stored in the capacitor.
A. 0.02 J
B. 0.04 J
C. 0.06 J
D. 0.08 J
Question 6
A particle of mass $m$ is attached to a spring with spring cons\tant $k$. The particle is displaced from its equilibrium position by a dis\tance $x_0$ and released from rest. Assuming the motion is simple harmonic, find the time $t$ at which the particle's kinetic energy is equal to its potential energy.
A. π/2ω
B. π/4ω
C. π/ω
D. 2π/ω
Question 7
A wave function is given by ( psi(x) = Ae^{ikx} ). If the wave function is normalized, what is the value of the cons\tant $A$?
A. \( A = \sqrt{\frac{1}{2pi}} \)
B. \( A = \sqrt{\frac{2pi}{1}} \)
C. \( A = \sqrt{\frac{1}{2pi}} + 1 \)
D. \( A = \sqrt{\frac{2pi}{1}} + 1 \)
Question 8
A gas at 300 K expands from 1 L to 2 L against a cons\tant external pressure of 1 atm. Calculate the work done by the gas.
A. 0.5 L atm
B. 1 L atm
C. 2 L atm
D. 3 L atm
Question 9
A wave function $\psi(x)$ is given by $\psi(x) = Ae^{ikx}$. Find the probability density $\rho(x)$ of the wave function.
A. |A|^2
B. A^2
C. Ae^{ikx}
D. Ae^{-ikx}
Question 10
A 50 Hz AC generator produces an emf given by \( epsilon = 120 \sin \( 2 pi ft \ \) ), where ( f ) is the frequency in Hz and ( t ) is time in seconds. If the maximum emf is 100 V, what is the value of ( f )?
A. 20 Hz
B. 25 Hz
C. 30 Hz
D. 50 Hz
Question 11
A convex lens of focal length 20 cm forms an image of an object placed 30 cm from the lens. If the object is moved to a dis\tance of 40 cm from the lens, what is the new image dis\tance?
A. 10 cm
B. 20 cm
C. 30 cm
D. 40 cm
Question 12
A circuit consists of a 100 Ω resistor, a 200 Ω resistor, and a 100 μF capacitor connected in series. Calculate the time cons\tant of the circuit.
A. 0.1 s
B. 0.2 s
C. 0.5 s
D. 1 s
Question 13
A 2 kg block is attached to a horizontal spring with a force cons\tant of 100 N/m. If the block is displaced by 5 cm from its equilibrium position and released, what is the maximum speed of the block?
A. 0.5 m/s
B. 1 m/s
C. 1.5 m/s
D. 2 m/s
Question 14
A magnetic field is produced by a current-carrying wire. If the current is $I$ and the dis\tance from the wire is $r$, what is the magnitude of the magnetic field?
A. \( \frac{mu_0 I}{2pi r} \)
B. \( \frac{2pi r}{mu_0 I} \)
C. \( \frac{mu_0 I}{r} \)
D. \( \frac{r}{mu_0 I} \)
Question 15
A particle of mass $m$ is moving in a circular orbit of radius $r$ with angular velocity $\omega$. Find the force $F$ exerted on the particle by the centripetal acceleration.
A. mω^2r
B. mω^2/r
C. mv^2/r
D. mv^2ω/r

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