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POST UTME REDEEMERS UNIVERSITY 2021 Physics | Objective

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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_0\( x \ $ = \sqrt{\frac{2}{L}} \sinleft$ \frac{pi x}{L}\right $). What is the expectation value of the position operator for this state?

Correct A. $ \frac{L}{2} $

B. $ \frac{L}{pi} $

C. $ \frac{2L}{pi} $

D. $ \frac{3L}{pi} $

Correct Answer: A

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Question 2

A block of mass $M$ is placed on a frictionless surface and attached to a horizontal spring with spring cons\tant $k$. The block is displaced by a dis\tance $x$ from its equilibrium position and released from rest. What is the angular frequency of the resulting simple harmonic motion?

Correct A. $ \sqrt{\frac{k}{M}} $

B. $ \frac{k}{M} $

C. $ \frac{M}{k} $

D. $ \frac{2k}{M} $

Correct Answer: A

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Question 3

A particle of mass $m$ is moving in a circular orbit of radius $r$ with a cons\tant speed $v$. What is the magnitude of the centripetal acceleration of the particle?

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

B. $ \frac{r^2}{v} $

C. $ \frac{v}{r} $

D. $ \frac{r}{v} $

Correct Answer: A

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Question 4

A projectile is launched from the origin with an initial velocity $v_0$ at an angle $\theta$ above the horizontal. What is the maximum height reached by the projectile?

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

B. $ \frac{v_0^2 \cos^2 \theta}{2g} $

C. $ \frac{v_0^2 \sin \theta}{2g} $

D. $ \frac{v_0^2 \cos \theta}{2g} $

Correct Answer: A

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Question 5

A wave of frequency $f$ and wavelength $lambda$ is traveling through a medium with speed $v$. What is the angular frequency of the wave?

Correct A. ( 2pi f )

B. $ \frac{2pi f}{lambda} $

C. $ \frac{lambda}{2pi f} $

D. $ \frac{v}{2pi f} $

Correct Answer: A

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Question 6

A particle of mass $m$ is confined to a one-dimensional box of length $L$. If the particle is in the ground state, what is the expectation value of its position?

Correct A. \frac{L}{2}

B. \frac{L}{4}

C. \frac{3L}{4}

D. \frac{L}{4}

Correct Answer: A

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Question 7

A gas is heated from $20^\circ\text{C}$ to $50^\circ\text{C}$. If the volume of the gas is doubled, what is the new pressure?

A. \frac{P_0}{2}

B. P_0

C. 2P_0

Correct D. 4P_0

Correct Answer: D

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Question 8

A charged particle of mass $m$ and charge $q$ is moving in a uniform magnetic field $\vec{B}$. If the particle is moving in a circular path of radius $R$, what is the speed of the particle?

Correct A. \frac{qBR}{m}

B. \frac{qB}{m}

C. \frac{m}{qB}

D. \frac{q}{mB}

Correct Answer: A

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Question 9

A simple p\endulum of length $L$ is released from an angle $\theta_0$ from the vertical. If the p\endulum is released from rest, what is the angular frequency of the p\endulum?

Correct A. \sqrt{\frac{g}{L}}

B. \sqrt{\frac{L}{g}}

C. \frac{g}{L}

D. \frac{L}{g}

Correct Answer: A

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Question 10

A heat engine operates between two temperatures $T_1$ and $T_2$. If the engine is 30% efficient, what is the ratio of the temperatures?

Correct A. \frac{T_2}{T_1} = 0.7

B. \frac{T_2}{T_1} = 0.3

C. \frac{T_2}{T_1} = 1.4

D. \frac{T_2}{T_1} = 1.7

Correct Answer: A

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Question 11

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 position of the particle?

Correct A. L/2

B. nL/\pi

C. L/\pi

D. nL/2\pi

Correct Answer: A

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Question 12

A block of mass $M$ is placed on a frictionless surface and connected to a horizontal spring with spring cons\tant $k$. The block is displaced by a dis\tance $x$ and released from rest. What is the angular frequency of the resulting simple harmonic motion?

Correct A. \sqrt{k/M}

B. k/M

C. 2\sqrt{k/M}

D. M/k

Correct Answer: A

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Question 13

A magnetic field of magnitude $B$ is directed perp\endicular to the plane of a circular loop of radius $r$. The loop carries a current $I$. What is the magnitude of the magnetic moment of the loop?

Correct A. I\pi r^2

B. I\pi r

C. I\pi r^3

D. I\pi r^4

Correct Answer: A

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Question 14

A sound wave with frequency $f$ is traveling through a medium with speed $v$. What is the wavelength of the sound wave?

Correct A. v/f

B. f/v

C. 2\pi v/f

D. 2\pi f/v

Correct Answer: A

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Question 15

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

Correct A. mv^2/r

B. mv/r

C. mvr

D. mv^2r

Correct Answer: A

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Question 16

A 2.0 mH inductor is connected in series with a 3.0 Ω resistor and a 12 V battery. If the initial current is 0 A, what is the current after 0.1 s?

A. 0.5 A

Correct B. 1.0 A

C. 1.5 A

D. 2.0 A

Correct Answer: B

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Question 17

A particle of mass 0.5 kg is attached to a spring with a spring cons\tant of 100 N/m. If the particle is displaced by 0.2 m from its equilibrium position and released from rest, what is its angular frequency?

A. 10 rad/s

B. 20 rad/s

Correct C. 30 rad/s

D. 40 rad/s

Correct Answer: C

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Question 18

A 10 Ω resistor is connected in parallel with a 20 Ω resistor. What is the equivalent resis\tance?

A. 5 Ω

B. 10 Ω

Correct C. 15 Ω

D. 20 Ω

Correct Answer: C

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Question 19

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. 12.5 Bq

Correct B. 25 Bq

C. 50 Bq

D. 100 Bq

Correct Answer: B

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Question 20

A 5.0 mH inductor is connected in series with a 2.0 Ω resistor and a 12 V battery. If the initial current is 0 A, what is the current after 0.2 s?

A. 0.5 A

B. 1.0 A

C. 1.5 A

Correct D. 2.0 A

Correct Answer: D

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Question 21

A 2.5 m long wire is made of a material with a resistivity of 2.1 × 10^$ -8 $ Ωm. If the wire is stretched to a length of 5 m, what is the new resis\tance?

A. 1.05 × 10^$ -7 $ Ω

B. 2.1 × 10^$ -7 $ Ω

Correct C. 4.2 × 10^$ -7 $ Ω

D. 5.25 × 10^$ -7 $ Ω

Correct Answer: C

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Question 22

A 100 V AC supply is connected to a 50 Ω resistor. If the current is 2 A, what is the power factor?

A. 0.5

Correct B. 0.6

C. 0.7

D. 0.8

Correct Answer: B

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Question 23

A particle moves in a circular path with a radius of 2 m. If it completes one revolution in 4 s, what is its angular velocity?

A. 0.5 rad/s

B. 1 rad/s

Correct C. 2 rad/s

D. 4 rad/s

Correct Answer: C

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Question 24

A 10 g sample of a radioactive subs\tance decays to 5 g in 2 hours. What is its half-life?

A. 1 hour

Correct B. 2 hours

C. 4 hours

D. 6 hours

Correct Answer: B

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Question 25

A 100 W heater is connected to a 230 V AC supply. If the current is 0.5 A, what is the power factor?

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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