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POST UTME PAN-ATLANTIC UNIVERSITY 2019 Physics | Objective

Are you preparing for POST UTME PAN-ATLANTIC UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2019 Physics (Objective) questions designed to simulate the real exam environment.

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Question 1

A particle of mass $m$ is confined to a one-dimensional box of length $L$. The ground state wave function of the particle is given by $psi_1(x) = \sqrt{\frac{2}{L}} \sinleft$ \frac{pi x}{L}\right $$. What is the expectation value of the position operator for this state?

A. 0

Correct B. \frac{L}{2}

C. L

D. \frac{3L}{4}

Correct Answer: B

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Question 2

A gas of $N$ non-interacting particles is confined to a volume $V$. The average kinetic energy of the particles is given by $\langle K \rangle = \frac{3}{2} N k_B T$. What is the average potential energy of the particles?

Correct A. \frac{3}{2} N k_B T

B. \frac{1}{2} N k_B T

C. 0

D. -\frac{1}{2} N k_B T

Correct Answer: A

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Question 3

A ray of light passes from air into a glass of re\fractive index $n$. The angle of incidence is $\theta_i$. What is the angle of re\fraction?

Correct A. \frac{n}{n_{air}} \theta_i

B. \frac{n_{air}}{n} \theta_i

C. \theta_i

D. \frac{\pi}{2} - \theta_i

Correct Answer: A

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Question 4

A spring of spring cons\tant $k$ is stretched by a dis\tance $x$. What is the potential energy stored in the spring?

Correct A. \frac{1}{2} k x^2

B. k x^2

C. k x

D. 0

Correct Answer: A

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Question 5

A particle of mass $m$ is moving in a circular orbit of radius $r$ with a speed $v$. What is the centripetal force acting on the particle?

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

B. \frac{m v}{r}

C. \frac{m r}{v}

D. 0

Correct Answer: A

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Question 6

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

B. 4 m/s

Correct C. 6 m/s

D. 8 m/s

Correct Answer: C

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Question 7

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 angle between the velocity vector and the radius vector at the ins\tant the particle is at the top of its circular path?

A. 30°

B. 45°

Correct C. 60°

D. 90°

Correct Answer: C

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Question 8

A 2.5 kg block is attached to a horizontal, massless spring with a force cons\tant of 400 N/m. The block is displaced by 0.1 m from its equilibrium position and released from rest. Assuming the block undergoes simple harmonic motion, calculate the total energy of the block at the ins\tant it passes through its equilibrium position.

A. 5 J

Correct B. 10 J

C. 15 J

D. 20 J

Correct Answer: B

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Question 9

A 3 kg block is moving in a circular path of radius 4 m with a cons\tant speed of 5 m/s. If the block is subjected to a centripetal force of 20 N, what is the angle between the velocity vector and the radius vector at the ins\tant the block is at the bottom of its circular path?

A. 60°

B. 75°

Correct C. 90°

D. 105°

Correct Answer: C

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Question 10

A 4 kg block is attached to a horizontal, massless spring with a force cons\tant of 600 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 acceleration of the block.

A. 20 m/s^2

B. 30 m/s^2

Correct C. 40 m/s^2

D. 50 m/s^2

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. If the particle is subjected to a centripetal acceleration of 2 m/s^2, what is the magnitude of the force acting on the particle?

A. 10 N

B. 12 N

Correct C. 8 N

D. 6 N

Correct Answer: C

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Question 12

A circuit consists of a 12 V battery, a 4 Ω resistor, and an inductor of induc\tance 2 H. If the circuit is closed at t = 0, what is the current in the circuit at t = 2 s?

A. 2 A

B. 3 A

Correct C. 1 A

D. 4 A

Correct Answer: C

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Question 13

A block of mass 5 kg is placed on a frictionless surface and a horizontal force of 10 N is applied to it. If the block is displaced by 2 m, what is the work done on the block?

Correct A. 20 J

B. 30 J

C. 40 J

D. 50 J

Correct Answer: A

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Question 14

A \tank is filled with water to a height of 4 m. If the density of water is 1000 kg/m^3, what is the pressure at the bottom of the \tank?

A. 40000 Pa

Correct B. 50000 Pa

C. 60000 Pa

D. 70000 Pa

Correct Answer: B

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Question 15

A spring has a spring cons\tant of 100 N/m. If a force of 50 N is applied to the spring, what is the displacement of the spring?

Correct A. 0.5 m

B. 0.6 m

C. 0.7 m

D. 0.8 m

Correct Answer: A

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Question 16

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

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

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

C. \frac{mv^2}{4r}

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

Correct Answer: A

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Question 17

A wave has a frequency of $f$ and a wavelength of $\lambda$. If the wave is reflected from a fixed \end, what is the new wavelength $\lambda'$?

Correct A. \frac{\lambda}{2}

B. \frac{2\lambda}{3}

C. \frac{3\lambda}{4}

D. \frac{4\lambda}{5}

Correct Answer: A

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Question 18

A radioactive sample has a half-life of $t_{1/2}$. If the sample is left for $3t_{1/2}$, what \fraction of the original sample remains?

Correct A. \frac{1}{8}

B. \frac{1}{4}

C. \frac{1}{2}

D. \frac{3}{4}

Correct Answer: A

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Question 19

A gas is heated from $T_1$ to $T_2$. If the volume of the gas is doubled, what is the new pressure $P'$?

Correct A. \frac{P}{2}

B. \frac{P}{4}

C. \frac{P}{8}

D. \frac{P}{16}

Correct Answer: A

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Question 20

A particle of mass $m$ is moving in a simple harmonic motion with a frequency $f$. If the amplitude of the motion is doubled, what is the new maximum kinetic energy $K'$?

Correct A. \frac{K}{2}

B. \frac{K}{4}

C. \frac{K}{8}

D. \frac{K}{16}

Correct Answer: A

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Question 21

A 1000 Ω resistor is connected in series with a 2000 Ω resistor and a 5 V battery. If the current through the 1000 Ω resistor is 0.5 A, what is the current through the 2000 Ω resistor?

A. 1 A

Correct B. 2 A

C. 3 A

D. 4 A

Correct Answer: B

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Question 22

A capacitor of capaci\tance 2 μF is connected in parallel with a 4 μF capacitor. What is the equivalent capaci\tance?

A. 2 μF

B. 4 μF

Correct C. 6 μF

D. 8 μF

Correct Answer: C

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Question 23

A 10 g sample of a gas at 300 K and 1 atm is heated to 400 K at cons\tant volume. What is the final pressure?

A. 1.5 atm

B. 2 atm

Correct C. 2.5 atm

D. 3 atm

Correct Answer: C

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Question 24

A 50 Ω resistor is connected in series with a 20 Ω resistor and a 10 V battery. If the current through the 50 Ω resistor is 0.2 A, what is the voltage across the 20 Ω resistor?

A. 2 V

Correct B. 4 V

C. 6 V

D. 8 V

Correct Answer: B

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Question 25

A capacitor of capaci\tance 10 μF is connected in series with a 100 Ω resistor and a 5 V battery. If the current through the capacitor is 0.1 A, what is the time cons\tant?

A. 10 s

Correct B. 20 s

C. 30 s

D. 40 s

Correct Answer: B

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