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POST UTME FUTO 2023 Physics | Objective

Are you preparing for POST UTME FUTO exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2023 Physics (Objective) questions designed to simulate the real exam environment.

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Question 1

A particle of mass 2 kg is moving in a circular orbit of radius 3 m with a speed of 4 m/s. If the particle is subject to a centripetal force of 10 N, what is the angular velocity of the particle?

A. 2 rad/s

Correct B. 4 rad/s

C. 6 rad/s

D. 8 rad/s

Correct Answer: B

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Question 2

A gas is enclosed in a container of volume 2 m^3 at a temperature of 300 K. If the gas is heated to a temperature of 400 K, what is the new volume of the gas?

A. 2.5 m^3

B. 3 m^3

Correct C. 3.5 m^3

D. 4 m^3

Correct Answer: C

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Question 3

A projectile is launched from the ground with an initial velocity of 20 m/s at an angle of 30° above the horizontal. If the projectile lands 10 m away from the launch point, what is the time of flight?

A. 1 s

Correct B. 2 s

C. 3 s

D. 4 s

Correct Answer: B

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Question 4

A heat engine operates between two temperatures of 500 K and 300 K. If the engine produces 100 J of work per cycle, what is the efficiency of the engine?

A. 0.2

B. 0.3

Correct C. 0.4

D. 0.5

Correct Answer: C

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Question 5

A simple harmonic motion has a frequency of 2 Hz and an amplitude of 3 m. If the motion is damped by a force proportional to the velocity, what is the equation of motion?

Correct A. x(t) = 3 e^{-0.5 t} \cos$ 2\pi t + \pi/2 $

B. x(t) = 3 e^{-0.5 t} \cos$ 2\pi t + \pi $

C. x(t) = 3 e^{-0.5 t} \cos$ 2\pi t $

D. x(t) = 3 e^{-0.5 t} \sin$ 2\pi t $

Correct Answer: A

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Question 6

A particle of mass $m$ is confined to a one-dimensional box of length $L$. U\sing the time-indep\endent Schrödinger equation, derive an expression for the energy levels of the particle.

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

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

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

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

Correct Answer: A

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Question 7

A block of mass $M$ is placed on a horizontal surface with a coefficient of static friction $\mu_s$. A horizontal force $F$ is applied to the block. If the block is at rest, what is the maximum value of $F$ that will cause the block to move?

Correct A. \mu_sMg

B. \mu_sMg/2

C. \mu_sMg/3

D. \mu_sMg/4

Correct Answer: A

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Question 8

A magnetic field $B$ is directed perp\endicular to a plane containing a current $I$. What is the direction of the magnetic field $B'$ produced by the current $I$?

Correct A. Clockwise

B. Counterclockwise

C. Into the page

D. Out of the page

Correct Answer: A

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Question 9

A beam of light passes from air into a medium with re\fractive index $n$. What is the angle of re\fraction $\theta'$?

Correct A. \frac{n}{n'}\theta

B. \frac{n'}{n}\theta

C. \frac{n}{n'-n}\theta

D. \frac{n'-n}{n}\theta

Correct Answer: A

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Question 10

A lens of focal length $f$ is placed in a beam of light. What is the image dis\tance $d'$?

Correct A. \frac{fd}{f-d}

B. \frac{fd}{f+d}

C. \frac{f-d}{fd}

D. \frac{f+d}{fd}

Correct Answer: A

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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 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 12

A parallel plate capacitor has a capaci\tance of 5 μF and is charged to a potential difference of 10 V. If the plates are separated by a dis\tance of 2 mm, what is the surface charge density on the plates?

A. 2.5 x 10^$ -3 $ C/m^2

Correct B. 5 x 10^$ -3 $ C/m^2

C. 7.5 x 10^$ -3 $ C/m^2

D. 10 x 10^$ -3 $ C/m^2

Correct Answer: B

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Question 13

A ray of light passes through a prism and is re\fracted at an angle of 30°. If the angle of incidence is 20°, what is the angle of re\fraction?

A. 10°

B. 20°

Correct C. 30°

D. 40°

Correct Answer: C

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Question 14

A particle of mass 1 kg is moving in a straight line with an initial velocity of 5 m/s. If it experiences a cons\tant acceleration of 2 m/s^2, what is its velocity after 3 seconds?

A. 7 m/s

B. 9 m/s

Correct C. 11 m/s

D. 13 m/s

Correct Answer: C

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Question 15

A parallel plate capacitor has a capaci\tance of 10 μF and is charged to a potential difference of 20 V. If the plates are separated by a dis\tance of 4 mm, what is the surface charge density on the plates?

A. 5 x 10^$ -3 $ C/m^2

Correct B. 10 x 10^$ -3 $ C/m^2

C. 15 x 10^$ -3 $ C/m^2

D. 20 x 10^$ -3 $ C/m^2

Correct Answer: B

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Question 16

A uniform magnetic field of strength 2 T is applied to a current-carrying wire. If the current in the wire is 5 A, what is the magnitude of the magnetic force per unit length on the wire?

A. 10 N/A

Correct B. 20 N/A

C. 30 N/A

D. 40 N/A

Correct Answer: B

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Question 17

A radioactive sample has a half-life of 10 years. If the initial activity is 100 Bq, what is the activity after 20 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 100 Ω resistor is connected in series with a 50 Ω resistor and a 20 Ω resistor. What is the equivalent resis\tance?

A. 50 Ω

B. 70 Ω

C. 100 Ω

Correct D. 170 Ω

Correct Answer: D

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Question 19

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 0.5 m from its equilibrium position, what is the magnitude of the force exerted on the particle?

A. 25 N

B. 50 N

C. 75 N

Correct D. 100 N

Correct Answer: D

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Question 20

A 10 kg block is susp\ended from a spring with a spring cons\tant of 50 N/m. If the block is displaced by 0.2 m from its equilibrium position, what is the magnitude of the force exerted on the block?

A. 5 N

B. 10 N

Correct C. 15 N

D. 20 N

Correct Answer: C

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Question 21

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 operator for this particle?

Correct A. L/2

B. nπL/2

C. L/2 + nπL/2

D. nπL/2 + L/2

Correct Answer: A

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Question 22

A radioactive sample decays according to the equation $N(t) = N_0 e^{-lambda t}$, where $N_0$ is the initial number of nuclei, $lambda$ is the decay cons\tant, and $t$ is time. If the half-life of the sample is 10 minutes, what is the decay cons\tant?

Correct A. 0.0693 min^-1

B. 0.693 min^-1

C. 6.93 min^-1

D. 69.3 min^-1

Correct Answer: A

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Question 23

A sound wave with frequency 200 Hz and amplitude 0.5 m is traveling through a medium with speed 343 m/s. What is the intensity of the sound wave?

Correct A. 0.5 W/m^2

B. 5 W/m^2

C. 50 W/m^2

D. 500 W/m^2

Correct Answer: A

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Question 24

A block of mass 5 kg is attached to a horizontal spring with spring cons\tant 100 N/m. The block is displaced by 0.2 m from its equilibrium position and released from rest. What is the maximum speed of the block?

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 25

A convex lens with focal length 20 cm is used to form an image of an object placed 30 cm from the lens. What is the magnification of the image?

Correct A. -0.5

B. -1

C. -2

D. -3

Correct Answer: A

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