POST UTME MOUNTAIN TOP UNIVERSITY 2022 Physics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A block of mass $m$ is placed on a frictionless surface and attached to a horizontal spring with spring cons\tant $k$. The block is displaced from its equilibrium position by a dis\tance $x_0$ and released from rest. Assuming the motion is simple harmonic, find the kinetic energy of the block as a function of time.
A. \frac{1}{2}m\omega^2x_0^2\sin^2\( \omega t \)
B. \frac{1}{2}m\omega^2x_0^2\cos^2\( \omega t \)
C. \frac{1}{2}m\omega^2x_0^2\sin\( \omega t \)
D. \frac{1}{2}m\omega^2x_0^2\cos\( \omega t \)
Question 2
A circuit consists of a resistor $R$ and an inductor $L$ connected in series. The circuit is driven by an alternating voltage source with a frequency $f$. Find the reac\tance of the inductor.
A. \omega L
B. \frac{1}{\omega L}
C. \sqrt{R^2 + \( \omega L \)^2}
D. \sqrt{R^2 - \( \omega L \)^2}
Question 3
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 angular frequency of the particle's motion.
A. \sqrt{\frac{k}{m}}
B. \frac{k}{m}
C. \frac{m}{k}
D. \frac{1}{\sqrt{mk}}
Question 4
A particle of mass $m$ is in a one-dimensional potential well of infinite height. Find the wave function of the particle.
A. \psi(x) = Ae^{-\frac{m}{\hbar^2}Vx}
B. \psi(x) = Ae^{\frac{m}{\hbar^2}Vx}
C. \psi(x) = Ae^{-\frac{m}{\hbar^2}Vx^2}
D. \psi(x) = Ae^{\frac{m}{\hbar^2}Vx^2}
Question 5
A circuit consists of a resistor $R$, an inductor $L$, and a capacitor $C$ connected in series. The circuit is driven by an alternating voltage source with a frequency $f$. Find the impedance of the circuit.
A. \sqrt{R^2 + \( \omega L - \frac{1}{\omega C} \)^2}
B. \sqrt{R^2 + \( \omega L + \frac{1}{\omega C} \)^2}
C. \sqrt{R^2 + \( \omega L - \frac{1}{\omega C} \)}
D. \sqrt{R^2 + \( \omega L + \frac{1}{\omega C} \)}

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