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POST UTME AAUA 2024 Physics | Objective

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Question 1

A particle of mass $m$ is confined to a one-dimensional box of length $L$. The wave function of the particle is given by (psi(x) = \sqrt{\frac{2}{L}} \sinleft$ \frac{npi x}{L}\right $). What is the expectation value of the position operator for this particle?

Correct A. L/2

B. nπL/2

C. nπL/2 + L/2

D. nπL/2 - L/2

Correct Answer: A

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Question 2

A ray of light passes from air into a glass of re\fractive index $n$. If the angle of incidence is $30^circ$, what is the angle of re\fraction?

Correct A. 20^circ

B. 30^circ

C. 40^circ

D. 50^circ

Correct Answer: A

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Question 3

A simple harmonic motion is described by the equation $x(t) = A \cos$ omega t + phi $$. If the amplitude is $A = 2$ cm, the angular frequency is $omega = 3$ rad/s, and the phase angle is $phi = pi/4$, what is the displacement of the particle at $t = 1$ s?

Correct A. 1.41 cm

B. 2.83 cm

C. 4.24 cm

D. 5.66 cm

Correct Answer: A

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Question 4

A nucleus of mass number $A$ and atomic number $Z$ undergoes \beta decay. What is the resulting nucleus?

Correct A. A-1, Z+1

B. A+1, Z-1

C. A, Z

D. A-1, Z-1

Correct Answer: A

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Question 5

A magnetic field is described by the equation $vec{B} = $ 2hat{i} + 3hat{j} $ \times 10^{-3}$ T. What is the magnitude of the magnetic field?

Correct A. 3.61 µT

B. 4.24 µT

C. 5.00 µT

D. 6.36 µT

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 centripetal force of 12 N, what is the magnitude of the acceleration of the particle?

A. 10 m/s^2

Correct B. 12 m/s^2

C. 15 m/s^2

D. 20 m/s^2

Correct Answer: B

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Question 7

A block of mass 5 kg is placed on a frictionless surface and connected 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, what is the maximum speed of the block?

A. 10 m/s

B. 15 m/s

Correct C. 20 m/s

D. 25 m/s

Correct Answer: C

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Question 8

A sound wave with a frequency of 200 Hz and a wavelength of 0.5 m is traveling through a medium. If the speed of the wave is 340 m/s, what is the amplitude of the wave?

Correct A. 0.05 m

B. 0.1 m

C. 0.15 m

D. 0.2 m

Correct Answer: A

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Question 9

A heat engine operates between two reservoirs at temperatures 500 K and 300 K. If the engine absorbs 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 10

A particle of mass 1 kg is moving in a circular path of radius 2 m with a cons\tant speed of 3 m/s. If the particle is subjected to a centripetal force of 6 N, what is the magnitude of the acceleration of the particle?

A. 6 m/s^2

B. 8 m/s^2

Correct C. 10 m/s^2

D. 12 m/s^2

Correct Answer: C

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Question 11

A solid sphere of radius 5 cm is floating in a liquid of density 0.8 g/cm³. If the density of the sphere is 2.5 g/cm³, what is the volume of the sphere?

A. 10 cm³

Correct B. 20 cm³

C. 30 cm³

D. 40 cm³

Correct Answer: B

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Question 12

A light ray 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 13

A capacitor consists of two parallel plates, each of area 0.1 m², separated by a dis\tance of 0.01 m. If the capaci\tance is 10 μF, what is the charge on the plates?

Correct A. 10 μC

B. 20 μC

C. 30 μC

D. 40 μC

Correct Answer: A

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Question 14

A magnetic field of strength 0.5 T is directed along the z-axis. If a current of 2 A flows in a wire loop of radius 0.1 m, what is the magnetic moment of the loop?

A. 0.1 A·m²

Correct B. 0.2 A·m²

C. 0.3 A·m²

D. 0.4 A·m²

Correct Answer: B

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Question 15

A lens of focal length 0.2 m is placed in a beam of light. If the object dis\tance is 0.5 m, what is the image dis\tance?

A. 0.1 m

B. 0.2 m

Correct C. 0.3 m

D. 0.4 m

Correct Answer: C

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Question 16

A particle of mass 2 kg is attached to a spring with spring cons\tant 100 N/m. It is displaced by 0.5 m from its equilibrium position and released from rest. Assuming the motion is simple harmonic, calculate the maximum kinetic energy of the particle.

A. 0.5 J

Correct B. 1 J

C. 1.5 J

D. 2 J

Correct Answer: B

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Question 17

A 10 μF capacitor is connected in series with a 50 Ω resistor and a 100 V battery. Calculate the time cons\tant of the circuit.

A. 0.5 s

Correct B. 1 s

C. 2 s

D. 5 s

Correct Answer: B

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Question 18

A magnetic field of 0.5 T is applied to a coil of 100 turns and 0.1 m radius. Calculate the induced emf in the coil.

A. 0.1 V

Correct B. 0.5 V

C. 1 V

D. 5 V

Correct Answer: B

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Question 19

A gas is heated from 300 K to 400 K at cons\tant volume. Calculate the change in internal energy.

A. 100 J

B. 200 J

Correct C. 300 J

D. 400 J

Correct Answer: C

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Question 20

A point charge of 2 μC is placed at the center of a conducting sphere of radius 0.1 m. Calculate the electric field at the surface of the sphere.

A. 10^4 N/C

B. 10^5 N/C

Correct C. 10^6 N/C

D. 10^7 N/C

Correct Answer: C

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Question 21

A parallel plate capacitor has a capaci\tance of 2 μF. If a potential difference of 10 V is applied across the plates, what is the charge stored on the capacitor?

A. 20 μC

Correct B. 40 μC

C. 60 μC

D. 80 μC

Correct Answer: B

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Question 22

A block of mass 5 kg is attached to a horizontal spring with a spring cons\tant of 200 N/m. If the block is displaced by 0.2 m from its equilibrium position and released, 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 23

A radioactive sample has a half-life of 10 years. If the initial activity is 100 Bq, what is the activity after 20 years?

A. 50 Bq

B. 25 Bq

C. 12.5 Bq

Correct D. 6.25 Bq

Correct Answer: D

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Question 24

A \tank is filled with water to a height of 5 m. If the density of water is 1000 kg/m^3, what is the pressure at the bottom of the \tank?

A. 5000 Pa

Correct B. 10000 Pa

C. 15000 Pa

D. 20000 Pa

Correct Answer: B

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Question 25

A simple p\endulum has a length of 1 m and a mass of 0.1 kg. If it is released from rest at an angle of 30° to the vertical, what is the time period of the p\endulum?

A. 2 s

B. 4 s

Correct C. 6 s

D. 8 s

Correct Answer: C

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