POST UTME ESUT 2022 Physics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A circuit consists of a 12 V battery, a 4 Ω resistor, and a 6 Ω resistor connected in series. What is the current flowing through the circuit?
A. 1 A
B. 2 A
C. 3 A
D. 4 A
Question 2
A sound wave of frequency $f$ is traveling through a medium. Find the wavelength of the wave.
A. \frac{v}{f}
B. \frac{f}{v}
C. fv
D. \frac{v}{f^2}
Question 3
A 10 μF capacitor is connected in series with a 100 Ω resistor and a 200 V battery. If the current in the circuit is 0.1 A, what is the time cons\tant of the circuit?
A. 0.1 s
B. 0.2 s
C. 0.5 s
D. 1 s
Question 4
A 2.5 kg block is attached to a horizontal, massless spring with a force cons\tant of 100 N/m. The block is displaced by 0.15 m from its equilibrium position and released from rest. Assuming the block undergoes simple harmonic motion, calculate the maximum speed of the block.
A. 1.5 m/s
B. 2.5 m/s
C. 3.5 m/s
D. 4.5 m/s
Question 5
A radioactive sample decays with a half-life of $T_{1/2}$. If the initial activity is $A_0$ and the time elapsed is $t$, what is the value of the activity $A$?
A. A_0 \left\( \frac{1}{2}\right \)^{t/T_{1/2}}
B. A_0 \left\( \frac{1}{2}\right \)^{T_{1/2}/t}
C. A_0 \left\( \frac{1}{2}\right \)^{t/2}
D. A_0 \left\( \frac{1}{2}\right \)^{2/T_{1/2}}
Question 6
A 1000 Ω resistor is connected in parallel with a 2000 Ω resistor. What is the equivalent resis\tance of the circuit?
A. 500 Ω
B. 1000 Ω
C. 2000 Ω
D. 4000 Ω
Question 7
A sound wave with frequency $f$ and amplitude $A$ is traveling through a medium with speed $v$. If the wave is reflected from a rigid surface, what is the frequency of the reflected wave?
A. f
B. 2f
C. \frac{v}{f}
D. \frac{f}{v}
Question 8
A gas at a pressure of 2 atm and a temperature of 300 K is allowed to expand to a pressure of 1 atm. What is the final temperature of the gas?
A. 200 K
B. 250 K
C. 300 K
D. 350 K
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 electric field $E$ between the plates?
A. \frac{Cd}{\epsilon_0A}
B. \frac{Q}{A\epsilon_0}
C. \frac{Cd}{A}
D. \frac{Q}{\epsilon_0A}
Question 10
A particle of mass $m$ is moving in a circular orbit of radius $r$ in a uniform magnetic field of strength $B$. If the particle's speed is $v$, what is the magnitude of the magnetic field?
A. \frac{mv}{qr}
B. \frac{mv^2}{qr}
C. \frac{m}{qr}
D. \frac{v}{qr}
Question 11
A particle of mass $m$ is projected from the origin with an initial velocity $v_0$ at an angle $\theta$ to the horizontal. The particle experiences a uniform gravitational field of magnitude $g$. Find the time $t$ at which the particle reaches its maximum height.
A. \frac{v_0 \sin \theta}{g}
B. \frac{v_0 \cos \theta}{g}
C. \frac{v_0 \sin \theta}{g^2}
D. \frac{v_0 \cos \theta}{g^2}
Question 12
A string of length $L$ is fixed at both \ends. The string is plucked at a point $\frac{L}{4}$ from one \end. Find the frequency of the fundamental mode.
A. \frac{1}{2L} \sqrt{\frac{T}{\mu}}
B. \frac{1}{4L} \sqrt{\frac{T}{\mu}}
C. \frac{1}{L} \sqrt{\frac{T}{\mu}}
D. \frac{1}{4L} \sqrt{\frac{T}{\mu^2}}
Question 13
A wave of frequency $f$ and wavelength $\lambda$ is traveling through a medium. Find the speed of the wave.
A. f\lambda
B. f + \lambda
C. f - \lambda
D. f\lambda^2
Question 14
A circuit consists of a $10\Omega$ resistor, a $5\mu F$ capacitor, and a $20\mu H$ inductor in series. The circuit is driven by a $10\,V$ AC source with a frequency of $50\,Hz$. Find the impedance of the circuit.
A. \sqrt{10^2 + \( 2\pi \times 50 \times 20 \times 10^{-6} - 2\pi \times 50 \times 5 \times 10^{-6} \)^2}
B. \sqrt{10^2 + \( 2\pi \times 50 \times 5 \times 10^{-6} - 2\pi \times 50 \times 20 \times 10^{-6} \)^2}
C. \sqrt{10^2 + \( 2\pi \times 50 \times 20 \times 10^{-6} + 2\pi \times 50 \times 5 \times 10^{-6} \)^2}
D. \sqrt{10^2 + \( 2\pi \times 50 \times 5 \times 10^{-6} + 2\pi \times 50 \times 20 \times 10^{-6} \)^2}
Question 15
A capacitor of capaci\tance $C$ is charged to a potential difference $V$. Find the energy stored in the capacitor.
A. \frac{1}{2} CV^2
B. CV^2
C. \frac{1}{4} CV^2
D. \frac{1}{8} CV^2

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