Practice post utme oau physics 2021 Past Questions

Question 1

A parallel beam of light of wavelength 500 nm is incident on a glass plate of re\fractive index 1.5. If the angle of incidence is 30°, calculate the angle of re\fraction.

Correct A. 20°

B. 30°

C. 40°

D. 50°

Correct Answer: A

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Question 2

A body of mass 2 kg is moving in a circular path of radius 3 m with a cons\tant speed of 4 m/s. Calculate the force acting on the body.

A. 10 N

B. 20 N

Correct C. 30 N

D. 40 N

Correct Answer: C

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Question 3

A particle of mass 1 kg is moving in a potential energy function given by U(x) = $ 1/2 $x^2 + 3x. Find the force acting on the particle at x = 2 m.

A. 2 N

B. 4 N

Correct C. 6 N

D. 8 N

Correct Answer: C

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Question 4

A circuit consists of a 2 Ω resistor, a 3 Ω resistor, and a 4 Ω resistor connected in series. If a voltage of 12 V is applied across the circuit, calculate the current flowing through the circuit.

A. 1 A

B. 2 A

Correct C. 3 A

D. 4 A

Correct Answer: C

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Question 5

A wave function is given by ψ(x) = Ae^$ -x^2/2a^2 $. If the wave function is normalized, find the value of a.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 6

A particle of mass $m$ is moving in a circular path of radius $r$ with a cons\tant speed $v$. If the particle is subject to a centripetal force $F_c = \frac{mv^2}{r}$, what is the magnitude of the acceleration of the particle?

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

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

C. \frac{mv^2}{r}

D. \frac{v^3}{r}

Correct Answer: A

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Question 7

A block of mass $m$ is placed on a frictionless surface and connected to a spring with a spring cons\tant $k$. If the block is displaced by a dis\tance $x$ from its equilibrium position and released, what is the frequency of the resulting simple harmonic motion?

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

B. \frac{k}{m}

C. \frac{m}{k}

D. \frac{\pi}{2}

Correct Answer: A

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Question 8

A parallel plate capacitor consists of two plates of area $A$ separated by a dis\tance $d$. If the capaci\tance of the capacitor is given by $C = \frac{\epsilon_0 A}{d}$, what is the capaci\tance of a capacitor with plates of area $4A$ and separation $2d$?

A. \frac{\epsilon_0 A}{d}

B. \frac{2\epsilon_0 A}{d}

C. \frac{\epsilon_0 4A}{2d}

Correct D. \frac{\epsilon_0 4A}{d}

Correct Answer: D

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Question 9

A beam of light is incident on a glass plate at an angle of incidence $\theta_i$. If the angle of re\fraction is $\theta_r$, what is the re\fractive index of the glass?

Correct A. \frac{\sin \theta_i}{\sin \theta_r}

B. \frac{\sin \theta_r}{\sin \theta_i}

C. \frac{\cos \theta_i}{\cos \theta_r}

D. \frac{\cos \theta_r}{\cos \theta_i}

Correct Answer: A

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Question 10

A particle of mass $m$ is moving in a circular path of radius $r$ with a cons\tant speed $v$. If the particle is subject to a centripetal force $F_c = \frac{mv^2}{r}$, what is the magnitude of the acceleration of the particle?

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

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

C. \frac{mv^2}{r}

D. \frac{v^3}{r}

Correct Answer: A

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Question 11

A block of mass 5 kg is attached to a horizontal, massless spring with a force cons\tant of 200 N/m. The block is displaced by 0.2 m from its equilibrium position and released from rest. Assuming the block undergoes simple harmonic motion, calculate the maximum speed of the block.

A. 2 m/s

Correct B. 4 m/s

C. 6 m/s

D. 8 m/s

Correct Answer: B

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Question 12

A gas is compressed from an initial volume of 0.5 m^3 to a final volume of 0.2 m^3 at a cons\tant temperature of 300 K. If the initial pressure is 100 kPa, calculate the final pressure of the gas.

A. 200 kPa

B. 250 kPa

Correct C. 300 kPa

D. 350 kPa

Correct Answer: C

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Question 13

A particle is moving in a circular path with a cons\tant speed of 4 m/s. If the radius of the circle is 2 m, calculate the centripetal acceleration of the particle.

A. 2 m/s^2

Correct B. 4 m/s^2

C. 6 m/s^2

D. 8 m/s^2

Correct Answer: B

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Question 14

A magnet is placed near a coil of wire, cau\sing a current to flow in the coil. If the magnetic field strength is 0.5 T and the coil has a resis\tance of 10 Ω, calculate the induced emf in the coil.

A. 0.5 V

Correct B. 1 V

C. 2 V

D. 5 V

Correct Answer: B

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Question 15

A block of wood is floating in a \tank of water. If the block has a mass of 2 kg and the density of water is 1000 kg/m^3, calculate the volume of the block.

A. 0.002 m^3

B. 0.004 m^3

Correct C. 0.006 m^3

D. 0.008 m^3

Correct Answer: C

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Question 16

A 2.5 mH inductor is connected in series with a 10 Ω resistor and a 20 V AC source. If the frequency of the source is 50 Hz, calculate the impedance of the circuit.

A. 15 Ω

B. 20 Ω

Correct C. 25 Ω

D. 30 Ω

Correct Answer: C

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Question 17

A particle of mass 0.5 kg is projected from the origin with an initial velocity of 20 m/s at an angle of 60° to the horizontal. Find the time of flight.

A. 1.5 s

Correct B. 2.0 s

C. 2.5 s

D. 3.0 s

Correct Answer: B

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Question 18

A parallel plate capacitor has a capaci\tance of 10 μF and is charged to a potential difference of 20 V. If a dielectric slab of thickness 2 mm and dielectric cons\tant 3 is inserted between the plates, find the new capaci\tance.

A. 15 μF

B. 20 μF

Correct C. 25 μF

D. 30 μF

Correct Answer: C

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Question 19

A block of mass 2 kg is susp\ended from a spring with a spring cons\tant of 100 N/m. If the block is displaced by 0.2 m from its equilibrium position and released, find the maximum velocity.

A. 2 m/s

B. 3 m/s

Correct C. 4 m/s

D. 5 m/s

Correct Answer: C

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Question 20

A \tank is filled with water to a height of 5 m. If a small hole of area 0.01 m^2 is made at the bottom of the \tank, find the rate at which the water level falls.

A. 0.1 m/s

Correct B. 0.2 m/s

C. 0.3 m/s

D. 0.4 m/s

Correct Answer: B

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Question 21

A 2.0 kg block is attached to a horizontal, massless spring with a force cons\tant of 100 N/m. The block is displaced by 0.20 m from its equilibrium position and released from rest. Assuming the block undergoes simple harmonic motion, determine the maximum speed of the block.

A. 0.50 m/s

B. 1.00 m/s

Correct C. 1.41 m/s

D. 2.00 m/s

Correct Answer: C

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Question 22

A parallel plate capacitor consists of two plates, each of area 0.10 m^2, separated by a dis\tance of 0.02 m. The capacitor is charged to a potential difference of 10 V. Determine the capaci\tance of the capacitor.

A. 0.50 F

B. 1.00 F

Correct C. 2.00 F

D. 4.00 F

Correct Answer: C

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Question 23

A 100 W light bulb is connected to a 120 V power source. Determine the current flowing through the bulb.

A. 0.50 A

Correct B. 1.00 A

C. 2.00 A

D. 4.00 A

Correct Answer: B

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Question 24

A wave has a frequency of 50 Hz and a wavelength of 2.0 m. Determine the speed of the wave.

A. 100 m/s

Correct B. 200 m/s

C. 500 m/s

D. 1000 m/s

Correct Answer: B

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Question 25

A 5.0 kg block is moving at a speed of 2.0 m/s. Determine the kinetic energy of the block.

A. 10 J

Correct B. 20 J

C. 50 J

D. 100 J

Correct Answer: B

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