Practice post utme oau physics 2022 Past Questions

Question 1

A ray of light passes through a prism and is re\fracted. The angle of incidence is 30°, and the angle of re\fraction is 20°. What is the angle of deviation?

A. 40°

B. 50°

Correct C. 60°

D. 70°

Correct Answer: C

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Question 2

A body of mass 5 kg is moving with a velocity of 10 m/s. What is its kinetic energy?

A. 50 J

Correct B. 100 J

C. 150 J

D. 200 J

Correct Answer: B

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Question 3

A lens has a focal length of 20 cm. An object is placed 30 cm in front of the lens. What is the image dis\tance?

A. 10 cm

B. 20 cm

C. 30 cm

Correct D. 40 cm

Correct Answer: D

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Question 4

A body is moving with a uniform acceleration of 2 m/s². Its initial velocity is 5 m/s. What is its velocity after 3 seconds?

A. 7 m/s

B. 8 m/s

Correct C. 9 m/s

D. 10 m/s

Correct Answer: C

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Question 5

A ray of light passes through a prism and is re\fracted. The angle of incidence is 30°, and the angle of re\fraction is 20°. What is the angle of deviation?

A. 40°

B. 50°

Correct C. 60°

D. 70°

Correct Answer: C

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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 angular frequency of the oscillations.

Correct A. \sqrt{\frac{k}{m}}

B. \frac{k}{m}

C. \frac{m}{k}

D. \frac{1}{\sqrt{mk}}

Correct Answer: A

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Question 7

A radioactive sample has a half-life of $T_{1/2}$. If the initial activity is $A_0$, find the activity after a time $t$.

Correct 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/T_{1/2}} + A_0

D. A_0 \left$ \frac{1}{2}\right $^{T_{1/2}/t}

Correct Answer: A

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Question 8

A wave has a frequency of $f$ and a wavelength of $\lambda$. Find the speed of the wave.

Correct A. f\lambda

B. f/\lambda

C. \lambda/f

D. 1/$ f\lambda $

Correct Answer: A

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Question 9

A particle of mass $m$ is moving in a circular orbit of radius $r$ with a speed $v$. Find the centripetal acceleration.

Correct A. \frac{v^2}{r}

B. \frac{r}{v^2}

C. \frac{m}{r}

D. \frac{r}{m}

Correct Answer: A

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Question 10

A wave has a frequency of $f$ and a speed of $v$. Find the wavelength.

Correct A. v/f

B. f/v

C. 1/$ v/f $

D. v/$ f^2 $

Correct Answer: A

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Question 11

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.

Correct A. \sqrt{\frac{k}{m}}

B. \frac{k}{m}

C. \frac{m}{k}

D. \frac{1}{\sqrt{km}}

Correct Answer: A

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Question 12

A sound wave with frequency $f$ is traveling through a medium with speed $v$. If the wavelength of the sound wave is $\lambda$, find the period of the sound wave.

Correct A. \frac{\lambda}{v}

B. \frac{v}{\lambda}

C. \frac{1}{f}

D. \frac{1}{v}

Correct Answer: A

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Question 13

A circuit consists of a resistor $R$, an inductor $L$, and a capacitor $C$ connected in series. If the circuit is driven by an alternating current source with angular frequency $\omega$, find the impedance of the circuit.

Correct A. \sqrt{R^2 + $ \omega L - \frac{1}{\omega C} $^2}

B. R + \omega L - \frac{1}{\omega C}

C. R - \omega L + \frac{1}{\omega C}

D. \frac{1}{R} + \frac{1}{\omega L} + \frac{1}{\omega C}

Correct Answer: A

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Question 14

A gas is contained in a cylinder with a movable piston. If the gas is heated, the piston moves and the volume of the gas increases. Assuming the gas is ideal, find the change in internal energy of the gas.

Correct A. nC_v\Delta T

B. nC_p\Delta T

C. nR\Delta T

D. nC_v\Delta V

Correct Answer: A

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Question 15

A transformer has a primary coil with $N_1$ turns and a secondary coil with $N_2$ turns. If the primary coil is connected to an alternating current source with voltage $V_1$ and the secondary coil is connected to a load with resis\tance $R$, find the current in the secondary coil.

Correct A. \frac{N_1}{N_2}\frac{V_1}{R}

B. \frac{N_2}{N_1}\frac{V_1}{R}

C. \frac{N_1}{N_2}\frac{R}{V_1}

D. \frac{N_2}{N_1}\frac{R}{V_1}

Correct Answer: A

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Question 16

A particle of mass $m$ is projected from the origin with an initial velocity $v_0$ at an angle $\theta$ to the horizontal. If the particle's trajectory is described by the equation $y = x \tan \theta - \frac{gx^2}{2v_0^2 \cos^2 \theta}$, where $g$ is the acceleration due to gravity, find the time $t$ at which the particle reaches its maximum height.

Correct A. $ t = \frac{v_0 \sin \theta}{g} $

B. $ t = \frac{v_0 \cos \theta}{g} $

C. $ t = \frac{v_0 \sin \theta}{g} $

D. $ t = \frac{v_0 \cos \theta}{g} $

Correct Answer: A

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Question 17

A circuit consists of a resistor $R_1 = 10 \Omega$, an inductor $L = 5 \text{H}$, a capacitor $C = 2 \text{F}$, and a voltage source $V = 20 \text{V}$ in series. If the circuit is connected to a switch that is initially open, find the current $i(t)$ in the circuit at time $t = 2 \text{s}$ after the switch is closed.

Correct A. $ i(t) = \frac{V}{R_1} \left\( 1 - e^{-\frac{R_1}{L} t} \right $

B. $ i(t) = \frac{V}{R_1} \left\( 1 + e^{-\frac{R_1}{L} t} \right $

C. $ i(t) = \frac{V}{R_1} \left\( 1 - e^{-\frac{R_1}{C} t} \right $

D. $ i(t) = \frac{V}{R_1} \left\( 1 + e^{-\frac{R_1}{C} t} \right $

Correct Answer: A

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Question 18

A point charge $q$ is placed at the origin of a coordinate system. If the electric potential $V$ at a point $P$ is given by the equation $V = \frac{k q}{r}$, where $k$ is Coulomb's cons\tant and $r$ is the dis\tance from the charge to point $P$, find the electric field $E$ at point $P$.

Correct A. $ E = \frac{k q}{r^2} $

B. $ E = \frac{k q^2}{r} $

C. $ E = \frac{k q}{r^3} $

D. $ E = \frac{k q^2}{r^2} $

Correct Answer: A

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Question 19

A capacitor $C$ is connected to a battery $V$ through a switch $S$. If the capacitor is initially uncharged, find the charge $Q$ on the capacitor at time $t$ after the switch is closed.

Correct A. $ Q = C V \left\( 1 - e^{-\frac{t}{RC}} \right $

B. $ Q = C V \left\( 1 + e^{-\frac{t}{RC}} \right $

C. $ Q = C V \left\( 1 - e^{-\frac{t}{C}} \right $

D. $ Q = C V \left\( 1 + e^{-\frac{t}{C}} \right $

Correct Answer: A

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Question 20

A current $i$ is flowing through a resistor $R$ and a capacitor $C$ in series. If the voltage $V$ across the resistor is given by the equation $V = i R$, find the voltage $V$ across the capacitor.

Correct A. $ V = i R $

B. $ V = i R + i C $

C. $ V = i R - i C $

D. $ V = i R \left\( 1 - e^{-\frac{t}{RC}} \right $

Correct Answer: A

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Question 21

A 50 Hz AC voltage source has a peak value of 100 V. Calculate the root mean square (RMS) value of the voltage.

Correct A. 70.71 V

B. 50 V

C. 100 V

D. 141.42 V

Correct Answer: A

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Question 22

A particle moves in a circular path with a cons\tant speed of 5 m/s. If the radius of the circle is 2 m, calculate the centripetal acceleration of the particle.

A. 1 m/s^2

B. 2 m/s^2

C. 5 m/s^2

Correct D. 10 m/s^2

Correct Answer: D

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Question 23

A circuit consists of a 10 Ω resistor and a 20 Ω resistor connected in parallel. If the voltage across the circuit is 20 V, calculate the current through the 10 Ω resistor.

A. 0.5 A

Correct B. 1 A

C. 2 A

D. 4 A

Correct Answer: B

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Question 24

A 5 kg block is attached to a horizontal spring with a spring cons\tant of 100 N/m. If the block is displaced by 2 m from its equilibrium position, calculate the potential energy stored in the spring.

A. 100 J

B. 200 J

Correct C. 500 J

D. 1000 J

Correct Answer: C

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Question 25

A 10 μF capacitor is connected in series with a 20 Ω resistor. If the voltage across the circuit is 10 V, calculate the current through the circuit.

A. 0.5 A

Correct B. 1 A

C. 2 A

D. 4 A

Correct Answer: B

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