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POST UTME OAU 2018 Physics | Objective

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Question 1

A parallel plate capacitor has plates of area $A$ and separation $d$. If the capaci\tance is $C$, find the value of the dielectric cons\tant $kappa$.

Correct A. \frac{Cd}{\epsilon_0A}

B. \frac{\epsilon_0A}{Cd}

C. \frac{Cd}{\epsilon_0}

D. \frac{\epsilon_0}{Cd}

Correct Answer: A

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Question 2

A particle of mass $m$ is projected from the origin with an initial velocity $v_0$ at an angle $\theta$ to the horizontal. Find the time of flight.

Correct A. \frac{2v_0\sin\theta}{g}

B. \frac{v_0\sin\theta}{g}

C. \frac{2v_0\cos\theta}{g}

D. \frac{v_0\cos\theta}{g}

Correct Answer: A

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Question 3

A circuit consists of a $10\Omega$ resistor, a $20\Omega$ resistor, and a $5\Omega$ resistor connected in parallel. If the voltage across the $10\Omega$ resistor is $10V$, find the current through the $5\Omega$ resistor.

A. 0.2A

Correct B. 0.4A

C. 0.6A

D. 0.8A

Correct Answer: B

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Question 4

A beam of light passes from air into a glass of re\fractive index $\mu$. If the angle of incidence is $\theta_i$, find the angle of re\fraction $\theta_r$.

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

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

C. \frac{\sin\theta_r}{\mu\sin\theta_i}

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

Correct Answer: A

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Question 5

A magnetic field is produced by a current-carrying wire. If the current is $I$ and the dis\tance from the wire is $r$, find the magnetic field strength $B$.

Correct A. \frac{\mu_0I}{2\pi r}

B. \frac{2\pi r}{\mu_0I}

C. \frac{\mu_0I}{r}

D. \frac{r}{\mu_0I}

Correct Answer: A

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Question 6

A particle of mass 2 kg is moving in a circular path of radius 3 m with a cons\tant speed of 4 m/s. If the particle is subjected to a uniform magnetic field of 2 T, what is the magnitude of the magnetic force acting on the particle?

A. 8 N

B. 10 N

Correct C. 12 N

D. 16 N

Correct Answer: C

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Question 7

A 10 μF capacitor is connected in series with a 20 Ω resistor and a 100 V battery. If the switch is closed at t = 0, what is the time cons\tant of the circuit?

A. 0.2 s

Correct B. 0.4 s

C. 0.6 s

D. 0.8 s

Correct Answer: B

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Question 8

A radioactive sample has a half-life of 5 years. If the initial activity is 100 Bq, what is the activity after 10 years?

A. 12.5 Bq

Correct B. 25 Bq

C. 50 Bq

D. 100 Bq

Correct Answer: B

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Question 9

A particle of mass 1 kg is moving in a potential energy function U(x) = 2x^2 + 5x. If the particle is initially at x = 2 m, what is the force acting on the particle at x = 3 m?

A. 10 N

B. 20 N

Correct C. 30 N

D. 40 N

Correct Answer: C

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Question 10

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 and released from rest, what is the maximum speed of the block?

A. 4 m/s

B. 6 m/s

Correct C. 8 m/s

D. 10 m/s

Correct Answer: C

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Question 11

A radioactive sample of Uranium-238 undergoes \alpha decay. If the initial mass of the sample is 100 g, and the half-life of Uranium-238 is 4.5 billion years, calculate the mass of the sample after 9 billion years.

Correct A. 12.5 g

B. 25 g

C. 50 g

D. 100 g

Correct Answer: A

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Question 12

A gas is confined to a container with a volume of 2.5 L. If the temperature of the gas is increased from 20°C to 50°C, and the pressure is increased from 1 atm to 2 atm, calculate the new volume of the gas.

A. 5 L

Correct B. 10 L

C. 15 L

D. 20 L

Correct Answer: B

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Question 13

A beam of light passes from air into a glass block with a re\fractive index of 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 14

A particle is projected at an angle of 45° to the horizontal with an initial velocity of 20 m/s. If the acceleration due to gravity is 9.8 m/s², calculate the time of flight.

A. 2 s

Correct B. 4 s

C. 6 s

D. 8 s

Correct Answer: B

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Question 15

A heat engine operates between two temperatures of 300 K and 600 K. If the efficiency of the engine is 30%, calculate the work done per cycle.

A. 100 J

Correct B. 200 J

C. 300 J

D. 400 J

Correct Answer: B

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Question 16

A particle of mass 2 kg is moving in a circular path of radius 3 m with a cons\tant speed of 4 m/s. The particle is subject to a centripetal force of 12 N. What is the magnitude of the acceleration of the particle?

A. 4 m/s^2

B. 6 m/s^2

Correct C. 8 m/s^2

D. 10 m/s^2

Correct Answer: C

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Question 17

A heat engine operates between two reservoirs at temperatures 500 K and 300 K. The engine receives 1000 J of heat from the high-temperature reservoir. What is the efficiency of the engine?

A. 0.2

Correct B. 0.3

C. 0.4

D. 0.5

Correct Answer: B

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Question 18

A charged particle of mass 1 kg and charge 2 C is moving in a magnetic field of strength 5 T. The particle has a velocity of 3 m/s. What is the magnitude of the force acting on the particle?

A. 10 N

Correct B. 20 N

C. 30 N

D. 40 N

Correct Answer: B

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Question 19

A block of mass 5 kg is attached to a horizontal spring with a force cons\tant of 200 N/m. The block is displaced by 2 m from its equilibrium position and released from rest. What is the maximum speed of the block?

A. 2 m/s

B. 4 m/s

Correct C. 6 m/s

D. 8 m/s

Correct Answer: C

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Question 20

A parallel plate capacitor has a capaci\tance of 10 μF and is charged to a potential difference of 5 V. What is the energy stored in the capacitor?

A. 0.25 J

Correct B. 0.5 J

C. 1 J

D. 2 J

Correct Answer: B

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Question 21

A particle of mass 2 kg is moving in a circular path of radius 3 m with a cons\tant speed of 4 m/s. If the particle is subjected to a centripetal force of 12 N, what is the magnitude of the acceleration of the particle?

A. 8 m/s^2

B. 12 m/s^2

Correct C. 16 m/s^2

D. 20 m/s^2

Correct Answer: C

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Question 22

A capacitor of capaci\tance 10 μF is connected in series with a resistor of resis\tance 20 Ω. If a voltage of 50 V is applied across the circuit, what is the current flowing through the circuit?

A. 0.25 A

Correct B. 0.5 A

C. 1 A

D. 2 A

Correct Answer: B

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Question 23

A projectile is launched from the ground with an initial velocity of 20 m/s at an angle of 60° above the horizontal. If the acceleration due to gravity is 9.8 m/s^2, what is the maximum height reached by the projectile?

A. 10 m

B. 15 m

Correct C. 20 m

D. 25 m

Correct Answer: C

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Question 24

A current of 5 A flows through a wire of resis\tance 10 Ω. If the wire is connected to a power source of voltage 20 V, what is the power consumed by the wire?

A. 50 W

B. 100 W

Correct C. 150 W

D. 200 W

Correct Answer: C

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Question 25

A body of mass 5 kg is moving with a velocity of 10 m/s. If the body is subjected to a force of 20 N, what is the acceleration of the body?

A. 2 m/s^2

B. 4 m/s^2

Correct C. 6 m/s^2

D. 8 m/s^2

Correct Answer: C

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