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POST UTME FUTA 2019 Physics | Objective

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Question 1 View Details

A 1000 Hz AC voltage source is connected to a 50 Ω resistor in series with a 20 μF capacitor. What is the impedance of the circuit?

A. 50 Ω

B. 100 Ω

C. 200 Ω

Correct D. √$ 50^2 + \( 1/(2π × 1000 × 20 × 10^(-6 \ $))^2) Ω

Correct Answer: D

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Question 2 View Details

A gas at 300 K expands from 1 L to 2 L against a cons\tant external pressure of 1 atm. What is the work done by the gas?

A. 1.5 L atm

B. 3 L atm

C. 4.5 L atm

Correct D. 6 L atm

Correct Answer: D

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Question 3 View Details

A 2 kg object is moving in a circular path with a cons\tant speed of 4 m/s. What is the magnitude of the net force acting on the object?

A. 10 N

B. 20 N

Correct C. 30 N

D. 40 N

Correct Answer: C

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Question 4 View Details

A point charge of +2 μC is placed at the origin of a coordinate system. What is the electric potential at a point 0.5 m away from the charge?

A. 100 V

B. 200 V

C. 300 V

Correct D. 400 V

Correct Answer: D

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Question 5 View Details

A 5 Ω resistor is connected in series with a 20 Ω resistor and a 10 μF capacitor. What is the time cons\tant of the circuit?

A. 0.1 s

B. 0.2 s

C. 0.3 s

Correct D. 0.4 s

Correct Answer: D

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Question 6 View Details

A solid sphere of radius $R$ is made of a material with density $\rho$. It is susp\ended in a fluid of density $sigma$. The sphere is in equilibrium, and the force of buoyancy is equal to the weight of the sphere. What is the depth of the center of the sphere below the surface of the fluid?

A. R

B. \frac{R}{2}

Correct C. \frac{2R}{3}

D. \frac{3R}{4}

Correct Answer: C

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Question 7 View Details

A convex lens of focal length $f$ forms an image of an object at a dis\tance $u$ from the lens. The magnification of the lens is $M$. What is the relationship between $f$, $u$, and $M$?

Correct A. \frac{f}{u} = M

B. \frac{f}{M} = u

C. \frac{u}{f} = M

D. \frac{f}{M} = \frac{1}{u}

Correct Answer: A

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Question 8 View Details

A magnetic field of strength $B$ is directed along the $z$-axis. A current of $I$ flows in a circular loop of radius $r$ in the $xy$-plane. What is the magnitude of the magnetic moment of the loop?

Correct A. I \pi r^2

B. I \pi r

C. I r^2

D. I r

Correct Answer: A

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Question 9 View Details

A nucleus of mass number $A$ and atomic number $Z$ undergoes \beta decay. What is the resulting nucleus?

Correct A. $ A' = A, Z' = Z + 1 $

B. $ A' = A + 1, Z' = Z $

C. $ A' = A - 1, Z' = Z $

D. $ A' = A, Z' = Z - 1 $

Correct Answer: A

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Question 10 View Details

A particle of mass $m$ is in a one-dimensional box of length $L$. What is the energy of the particle in the ground state?

Correct A. \frac{h^2}{8mL^2}

B. \frac{h^2}{4mL^2}

C. \frac{h^2}{2mL^2}

D. \frac{h^2}{mL^2}

Correct Answer: A

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Question 11 View Details

A particle of mass $m$ is moving in a circular orbit of radius $r$ with a speed $v$. If the particle is subjected to a uniform magnetic field of strength $B$, what is the frequency of the radiation emitted by the particle as it moves through the magnetic field?

Correct A. $ f = \frac{qB}{2\pi m} $

B. $ f = \frac{qB}{4\pi m} $

C. $ f = \frac{qB}{6\pi m} $

D. $ f = \frac{qB}{8\pi m} $

Correct Answer: A

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Question 12 View Details

A gas is enclosed in a container of volume $V$ at a temperature $T$. If the gas is heated to a temperature $T + \Delta T$, what is the change in the pressure of the gas?

Correct A. $ \Delta P = \frac{nRT\Delta T}{V} $

B. $ \Delta P = \frac{nRT}{V} $

C. $ \Delta P = \frac{nRT\Delta T}{2V} $

D. $ \Delta P = \frac{nRT}{2V} $

Correct Answer: A

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Question 13 View Details

A wave of frequency $f$ and wavelength $\lambda$ is traveling through a medium with a speed $v$. If the wave is reflected from a surface, what is the frequency of the reflected wave?

Correct A. $ f' = f $

B. $ f' = 2f $

C. $ f' = \frac{f}{2} $

D. $ f' = \frac{f}{3} $

Correct Answer: A

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Question 14 View Details

A particle of mass $m$ is moving in a potential $U(x) = kx^2$. If the particle is released from rest at $x = 0$, what is the total energy of the particle?

Correct A. $ E = \frac{1}{2}mv^2 + U(x) $

B. $ E = \frac{1}{2}mv^2 - U(x) $

C. $ E = \frac{1}{2}mv^2 $

D. $ E = -U(x) $

Correct Answer: A

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Question 15 View Details

A gas is enclosed in a container of volume $V$ at a temperature $T$. If the gas is compressed to a volume $V/2$, what is the change in the pressure of the gas?

Correct A. $ \Delta P = \frac{nRT}{V} \Delta V $

B. $ \Delta P = \frac{nRT}{V} $

C. $ \Delta P = \frac{nRT\Delta V}{V} $

D. $ \Delta P = \frac{nRT}{2V} \Delta V $

Correct Answer: A

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Question 16 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. 2 m/s^2

B. 4 m/s^2

Correct C. 6 m/s^2

D. 8 m/s^2

Correct Answer: C

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Question 17 View Details

A magnetic field of 0.5 T is applied to a coil of wire with 100 turns. If the coil is connected to a battery of 12 V, what is the induced emf in the coil?

A. 0.6 V

B. 1.2 V

Correct C. 2.4 V

D. 3.6 V

Correct Answer: C

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Question 18 View Details

A radioactive sample has an initial activity of 100 Bq. If the half-life of the sample is 10 minutes, what is the activity of the sample after 30 minutes?

Correct A. 25 Bq

B. 50 Bq

C. 75 Bq

D. 100 Bq

Correct Answer: A

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Question 19 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. 20°

Correct B. 25°

C. 30°

D. 35°

Correct Answer: B

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Question 20 View Details

A projectile is launched at an angle of 45° with an initial velocity of 20 m/s. If the acceleration due to gravity is 9.8 m/s^2, what is the maximum height reached by the projectile?

A. 10 m

B. 15 m

Correct C. 20 m

D. 25 m

Correct Answer: C

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Question 21 View Details

A beam of light 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 22 View Details

A 5 μF capacitor is connected in series with a 10 kΩ resistor. If a 50 V battery is connected across the circuit, what is the time cons\tant of the circuit?

A. 0.1 s

Correct B. 0.5 s

C. 1 s

D. 2 s

Correct Answer: B

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Question 23 View Details

A particle of mass 2 kg is moving in a circular path of radius 3 m with a speed of 4 m/s. What is the centripetal 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 24 View Details

A wave has a frequency of 100 Hz and a wavelength of 0.5 m. What is the speed of the wave?

A. 50 m/s

Correct B. 100 m/s

C. 150 m/s

D. 200 m/s

Correct Answer: B

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Question 25 View Details

A 10 μF capacitor is connected in parallel with a 20 μF capacitor. What is the equivalent capaci\tance of the circuit?

A. 10 μF

B. 20 μF

Correct C. 30 μF

D. 40 μF

Correct Answer: C

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