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POST UTME COAL CITY UNIVERSITY 2019 Physics | Objective

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Question 1

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 as it passes through its equilibrium position.

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 2

A parallel plate capacitor consists of two plates, each of area 0.01 m^2, separated by a dis\tance of 0.001 m. The space between the plates is filled with a dielectric material of dielectric cons\tant 2.5. Calculate the capaci\tance of the capacitor.

A. 1.25 nF

Correct B. 2.5 nF

C. 5 nF

D. 10 nF

Correct Answer: B

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Question 3

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. Calculate the magnitude of the centripetal acceleration of the particle.

A. 0.5 m/s^2

B. 1 m/s^2

Correct C. 2 m/s^2

D. 4 m/s^2

Correct Answer: C

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Question 4

A body of mass 10 kg is moving with a velocity of 5 m/s. Calculate the kinetic energy of the body.

A. 25 J

Correct B. 50 J

C. 100 J

D. 200 J

Correct Answer: B

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Question 5

A heat engine operates between two temperatures of 500 K and 300 K. Calculate the efficiency of the engine.

A. 0.25

Correct B. 0.5

C. 0.75

D. 1

Correct Answer: B

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Question 6

A sound wave with a frequency of 200 Hz is produced by a source moving towards a stationary observer at a speed of 20 m/s. If the speed of sound in air is 340 m/s, calculate the apparent frequency heard by the observer.

A. 220 Hz

Correct B. 240 Hz

C. 260 Hz

D. 280 Hz

Correct Answer: B

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Question 7

A capacitor with capaci\tance 10 μF is connected in series with a resistor of 5 kΩ. If a voltage of 20 V is applied across the circuit, calculate the current flowing through the circuit.

A. 0.2 mA

B. 0.4 mA

Correct C. 0.6 mA

D. 0.8 mA

Correct Answer: C

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Question 8

A magnetic field of 0.5 T is produced by a current of 2 A flowing through a wire of length 1 m. If the wire is placed in a region of uniform magnetic field, calculate the force experienced by the wire.

Correct A. 0.5 N

B. 1 N

C. 1.5 N

D. 2 N

Correct Answer: A

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Question 9

A 10 μF capacitor is charged to a potential difference of 10 V. If the capacitor is then connected in parallel with a 20 μF capacitor, calculate the new potential difference across the capacitors.

A. 5 V

Correct B. 10 V

C. 15 V

D. 20 V

Correct Answer: B

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Question 10

A 50 Hz AC voltage is applied across a circuit containing a resistor of 10 kΩ and an inductor of 100 mH. If the circuit is initially at rest, calculate the current flowing through the circuit after 10 ms.

A. 0.1 A

B. 0.2 A

Correct C. 0.3 A

D. 0.4 A

Correct Answer: C

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Question 11

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. What is the magnitude of the force acting on the particle?

A. 16 N

Correct B. 32 N

C. 48 N

D. 64 N

Correct Answer: B

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Question 12

A capacitor consists of two parallel plates, each of area 0.1 m^2, separated by a dis\tance of 0.01 m. The plates are charged to a potential difference of 10 V. What is the capaci\tance of the capacitor?

Correct A. 0.1 F

B. 0.2 F

C. 0.3 F

D. 0.4 F

Correct Answer: A

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Question 13

A coil of wire has an induc\tance of 0.1 H and a resis\tance of 10 ohms. If a current of 2 A is passed through the coil, what is the energy stored in the coil?

Correct A. 0.1 J

B. 0.2 J

C. 0.3 J

D. 0.4 J

Correct Answer: A

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Question 14

A circuit consists of a 10 ohm resistor, a 20 ohm resistor, and a 5 ohm resistor connected in series. If a voltage of 20 V is applied across the circuit, what is the current flowing through the 5 ohm resistor?

A. 2 A

Correct B. 3 A

C. 4 A

D. 5 A

Correct Answer: B

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Question 15

A magnetic field of 0.1 T is applied to a coil of wire with an area of 0.01 m^2. If the coil has 100 turns, what is the magnetic flux through the coil?

Correct A. 0.1 Wb

B. 0.2 Wb

C. 0.3 Wb

D. 0.4 Wb

Correct Answer: A

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Question 16

A 1000 Hz AC voltage source is connected to a 50 Ω resistor. If the peak value of the voltage is 100 V, what is the average power dissipated in the resistor?

A. 250 W

Correct B. 500 W

C. 750 W

D. 1000 W

Correct Answer: B

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Question 17

A particle of mass 2 kg is attached to a spring with a spring cons\tant of 100 N/m. If the particle is displaced by 0.1 m from its equilibrium position and released from rest, what is the maximum speed of the particle?

A. 0.5 m/s

Correct B. 1.0 m/s

C. 1.5 m/s

D. 2.0 m/s

Correct Answer: B

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Question 18

A beam of light passes from air into a glass of re\fractive index 1.5. If the angle of incidence is 30°, what is the angle of re\fraction?

Correct A. 20°

B. 30°

C. 40°

D. 50°

Correct Answer: A

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Question 19

A radioactive sample has a half-life of 10 years. If the initial activity is 1000 Bq, what is the activity after 20 years?

A. 250 Bq

Correct B. 500 Bq

C. 750 Bq

D. 1000 Bq

Correct Answer: B

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Question 20

A wave function is given by ψ(x) = Ae^(ikx). If the wave function is normalized, what is the value of A?

Correct A. 1/√(2π)

B. 1/√(π)

C. 1/√(2)

D. 1/√(4)

Correct Answer: A

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Question 21

A particle of mass 2 kg is projected from the origin with an initial velocity of 10 m/s at an angle of 60° to the horizontal. If the particle experiences a uniform downward acceleration of 2 m/s² due to gravity, calculate the time taken for the particle to reach its maximum height.

A. 2.5 s

Correct B. 3.0 s

C. 3.5 s

D. 4.0 s

Correct Answer: B

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Question 22

A parallel plate capacitor consists of two plates, each of area 0.1 m², separated by a dis\tance of 0.01 m. The capaci\tance of the capacitor is 10 nF. If a potential difference of 10 V is applied across the plates, calculate the charge stored on each plate.

Correct A. 0.1 C

B. 0.2 C

C. 0.3 C

D. 0.4 C

Correct Answer: A

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Question 23

A radioactive sample decays at a rate given by the equation \( N(t) = N_0 e^{-\lambda t} \), where \( N(t) \) is the number of nuclei remaining at time \( t \), \( N_0 \) is the initial number of nuclei, and \( \lambda \) is the decay cons\tant. If \( N_0 = 1000 \) and \( \lambda = 0.1 \) s⁻¹, calculate the number of nuclei remaining after 5 s.

A. 100

B. 200

Correct C. 300

D. 400

Correct Answer: C

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Question 24

A gas expands from an initial volume of 0.1 m³ to a final volume of 0.5 m³ against a cons\tant external pressure of 10 kPa. If the work done by the gas is 50 J, calculate the change in internal energy of the gas.

Correct A. -50 J

B. -40 J

C. -30 J

D. -20 J

Correct Answer: A

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Question 25

A wave of frequency 100 Hz and wavelength 0.1 m is propagating through a medium. If the wave is reflected from a fixed \end, calculate the amplitude of the reflected wave.

A. 0.5 m

B. 0.6 m

Correct C. 0.7 m

D. 0.8 m

Correct Answer: C

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