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POST UTME FUTA 2022 Physics | Objective

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Question 1 View Details

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

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

B. \frac{v}{r}

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

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

Correct Answer: D

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Question 2 View Details

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

A. 20 \mu C

Correct B. 40 \mu C

C. 60 \mu C

D. 80 \mu C

Correct Answer: B

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Question 3 View Details

A ray of light passes from air into a glass slab of re\fractive index $n = 1.5$. If the angle of incidence is $30^\circ$, what is the angle of re\fraction?

A. 20^\circ

B. 30^\circ

Correct C. 40^\circ

D. 50^\circ

Correct Answer: C

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Question 4 View Details

A magnetic field is produced by a current-carrying wire. If the current is $I = 2 A$ and the length of the wire is $L = 1 m$, what is the magnitude of the magnetic field at a dis\tance $r = 0.5 m$ from the wire?

A. 0.02 T

Correct B. 0.04 T

C. 0.06 T

D. 0.08 T

Correct Answer: B

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Question 5 View Details

A lens has a focal length of $f = 20 cm$. If an object is placed at a dis\tance $u = 30 cm$ from the lens, what is the image dis\tance?

A. -10 cm

Correct B. -20 cm

C. -30 cm

D. -40 cm

Correct Answer: B

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Question 6 View Details

A gas at $25^circ$C is heated to $100^circ$C. If the initial volume is $2.5\text{ L}$, what is the final volume if the gas expands according to Charles' Law?

A. 3.125 L

Correct B. 4.1667 L

C. 5.2083 L

D. 6.25 L

Correct Answer: B

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Question 7 View Details

A particle of mass $m$ is moving in a circular path of radius $r$ with a cons\tant speed $v$. If the particle experiences a centripetal force $F_c = \frac{mv^2}{r}$, what is the work done by this force as the particle moves through an angle $\theta$?

Correct A. $F_c r \sin \theta$

B. $F_c r \cos \theta$

C. $F_c r \tan \theta$

D. $F_c r csc \theta$

Correct Answer: A

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Question 8 View Details

A block of mass $m$ is attached to a horizontal, massless spring with a spring cons\tant $k$. If the block is displaced by a dis\tance $x$ from its equilibrium position and released from rest, what is the maximum kinetic energy of the block?

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

B. $k x^2$

C. $\frac{1}{2} m x^2$

D. $m x^2$

Correct Answer: A

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Question 9 View Details

A heat engine operates between two reservoirs at temperatures $T_1 = 500\text{ K}$ and $T_2 = 300\text{ K}$. If the engine produces 500 J of work per cycle, what is the efficiency of the engine?

A. 25%

Correct B. 30%

C. 35%

D. 40%

Correct Answer: B

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Question 10 View Details

A particle of mass $m$ is moving in a straight line with an initial velocity $v_0$ and an initial position $x_0$. If the particle experiences a cons\tant acceleration $a$, what is the position of the particle at time $t$?

Correct A. $x_0 + v_0 t + \frac{1}{2} a t^2$

B. $x_0 + v_0 t - \frac{1}{2} a t^2$

C. $x_0 - v_0 t + \frac{1}{2} a t^2$

D. $x_0 - v_0 t - \frac{1}{2} a t^2$

Correct Answer: A

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Question 11 View Details

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. 4 m/s^2

B. 6 m/s^2

Correct C. 8 m/s^2

D. 10 m/s^2

Correct Answer: C

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Question 12 View Details

A block of mass 5 kg is placed on a frictionless surface and attached to a horizontal spring with a force cons\tant of 200 N/m. If 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

B. 4 m/s

Correct C. 6 m/s

D. 8 m/s

Correct Answer: C

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Question 13 View Details

A ray of light 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?

A. 10°

Correct B. 12°

C. 15°

D. 18°

Correct Answer: B

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Question 14 View Details

A lens of focal length 20 cm is used to form an image of an object placed 30 cm from the lens. If the object is moved to a dis\tance of 40 cm from the lens, what is the new image dis\tance?

A. 60 cm

Correct B. 80 cm

C. 100 cm

D. 120 cm

Correct Answer: B

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Question 15 View Details

A 60 Hz AC generator produces an emf of 120 V. If the generator is connected to a 10 Ω resistor, what is the maximum current in the circuit?

A. 10 A

B. 15 A

Correct C. 17 A

D. 20 A

Correct Answer: C

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Question 16 View Details

A particle of mass 2 kg is moving in a circular path with a radius of 3 m. If the particle experiences a centripetal acceleration of 4 m/s^2, what is its angular velocity?

A. 10 rad/s

Correct B. 20 rad/s

C. 30 rad/s

D. 40 rad/s

Correct Answer: B

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Question 17 View Details

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

A. 20°

Correct B. 25°

C. 30°

D. 35°

Correct Answer: B

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Question 18 View Details

A circuit consists of a 12 V battery, a 4 Ω resistor, and a 6 Ω resistor connected in series. What is the current flowing through the circuit?

A. 1.5 A

Correct B. 2 A

C. 2.5 A

D. 3 A

Correct Answer: B

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Question 19 View Details

A simple harmonic motion has a maximum displacement of 5 m and a period of 2 s. What is the angular frequency?

A. 1.25 rad/s

Correct B. 2.5 rad/s

C. 3.75 rad/s

D. 5 rad/s

Correct Answer: B

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Question 20 View Details

A light ray passes through a convex lens of focal length 20 cm. If the object dis\tance is 30 cm, what is the image dis\tance?

A. 10 cm

Correct B. 20 cm

C. 30 cm

D. 40 cm

Correct Answer: B

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