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POST UTME ACHIEVERS UNIVERSITY 2018 Physics | Objective

Are you preparing for POST UTME ACHIEVERS UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2018 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 wave function of the particle is given by $psi(x) = \sqrt{\frac{2}{L}} \sinleft$ \frac{npi x}{L}\right $$, where $n$ is a positive integer. What is the expectation value of the potential energy of the particle?

A. 0

Correct B. \frac{n^2\pi^2\hbar^2}{2mL^2}

C. \frac{n^2\pi^2\hbar^2}{mL^2}

D. \frac{n^2\pi^2\hbar^2}{2mL}

Correct Answer: B

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Question 2

A radioactive sample of $^{238}U$ has a half-life of $4.5 \times 10^9$ years. If the initial activity of the sample is $A_0 = 10^6$ Bq, what is the activity of the sample after $t = 10^9$ years?

A. 5 \times 10^5 Bq

Correct B. 2.5 \times 10^5 Bq

C. 1.25 \times 10^5 Bq

D. 6.25 \times 10^5 Bq

Correct Answer: B

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Question 3

A circuit consists of a 12 V battery, a 4 Ω resistor, and an inductor of induc\tance $L = 2$ H. The circuit is connected to a switch that is closed at time $t = 0$. What is the current in the circuit at time $t = 1$ s?

A. 3 A

B. 2 A

Correct C. 1 A

D. 4 A

Correct Answer: C

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Question 4

A capacitor of capaci\tance $C = 10$ μF is connected to a 12 V battery. What is the energy stored in the capacitor?

Correct A. 120 J

B. 60 J

C. 30 J

D. 15 J

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{mv^2}{r}

B. \frac{mv}{r}

C. \frac{m}{r}

D. \frac{r}{m}

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 acceleration of 2 m/s^2, what is the magnitude of the force acting on the particle?

A. 10 N

B. 20 N

Correct C. 30 N

D. 40 N

Correct Answer: C

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Question 7

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 8

A simple harmonic motion has a period of 2 s and an amplitude of 5 m. If the particle is at its maximum displacement at t = 0, what is its displacement at t = 1 s?

A. 2 m

Correct B. 3 m

C. 4 m

D. 5 m

Correct Answer: B

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Question 9

A force of 10 N is applied to a particle of mass 2 kg. If the particle is moving in a circular path of radius 3 m, what is the magnitude of the centripetal acceleration?

A. 2 m/s^2

B. 3 m/s^2

C. 4 m/s^2

Correct D. 5 m/s^2

Correct Answer: D

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Question 10

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

A. 20°

B. 30°

C. 40°

Correct D. 50°

Correct Answer: D

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Question 11

A particle of mass $m$ is moving in a circular orbit of radius $r$ under the influence of a central force given by $F(r) = \frac{k}{r^2}$. If the particle's speed is $v$, what is the magnitude of the force acting on it?

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

B. \frac{k}{r}

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

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

Correct Answer: A

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Question 12

A sound wave with frequency $f$ and amplitude $A$ is propagating through a medium with speed $v$. If the wave is reflected off a rigid surface, what is the frequency of the reflected wave?

A. f

Correct B. 2f

C. \frac{v}{f}

D. \frac{f}{v}

Correct Answer: B

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Question 13

A quantum particle of mass $m$ is confined to a one-dimensional box of length $L$. If the particle's energy is $E$, what is the wavelength of the particle?

Correct A. \frac{2\pi\hbar}{\sqrt{2mE}}

B. \frac{2\pi\hbar}{mE}

C. \frac{\sqrt{2mE}}{2\pi\hbar}

D. \frac{mE}{2\pi\hbar}

Correct Answer: A

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Question 14

A simple harmonic oscillator with mass $m$ and spring cons\tant $k$ is displaced from its equilibrium position by a dis\tance $x$. If the oscillator's angular frequency is $\omega$, what is the magnitude of the force acting on it?

Correct A. kx

B. \frac{k}{x}

C. \frac{m\omega^2}{k}

D. \frac{k}{m\omega^2}

Correct Answer: A

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Question 15

A fluid of density $\rho$ is confined to a vertical cylinder of radius $R$. If the fluid's pressure is $P$ at the bottom of the cylinder, what is the pressure at the top of the cylinder?

Correct A. P-\rho g h

B. P+\rho g h

C. P-\rho g R

D. P+\rho g R

Correct Answer: A

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Question 16

A 2 kg block of wood is heated from 20°C to 80°C. If the specific heat capacity of wood is 1.5 kJ/kg°C, calculate the heat energy required to heat the block.

A. 6 kJ

Correct B. 12 kJ

C. 18 kJ

D. 24 kJ

Correct Answer: B

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Question 17

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

Correct A. 12.5 Bq

B. 25 Bq

C. 50 Bq

D. 100 Bq

Correct Answer: A

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Question 18

A 10 kg block is placed on a frictionless surface. If a force of 20 N is applied to the block, what is the acceleration of the block?

A. 0.2 m/s^2

B. 1 m/s^2

C. 2 m/s^2

Correct D. 5 m/s^2

Correct Answer: D

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Question 19

A 5 kg block is attached to a spring with a spring cons\tant of 100 N/m. If the block is displaced by 0.2 m from its equilibrium position, what is the potential energy stored in the spring?

A. 1 J

B. 2 J

Correct C. 5 J

D. 10 J

Correct Answer: C

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Question 20

A magnetic field of 0.5 T is applied to a current-carrying wire. If the current is 2 A, what is the force experienced by the wire?

A. 0.1 N

Correct B. 0.5 N

C. 1 N

D. 2 N

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. 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 22

A wave has a frequency of 50 Hz and a wavelength of 0.2 m. What is the speed of the wave?

A. 10 m/s

B. 20 m/s

Correct C. 30 m/s

D. 40 m/s

Correct Answer: C

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Question 23

A body of mass 5 kg is moving with a velocity of 10 m/s. If it 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

C. 6 m/s^2

Correct D. 8 m/s^2

Correct Answer: D

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Question 24

A particle of mass 3 kg is moving in a circular path of radius 2 m with a cons\tant speed of 5 m/s. If the particle is subjected to a centripetal force of 15 N, what is the magnitude of the acceleration of the particle?

A. 5 m/s^2

B. 10 m/s^2

Correct C. 15 m/s^2

D. 20 m/s^2

Correct Answer: C

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Question 25

A wave has a frequency of 100 Hz and a wavelength of 0.1 m. What is the speed of the wave?

A. 20 m/s

B. 30 m/s

Correct C. 40 m/s

D. 50 m/s

Correct Answer: C

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