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POST UTME FUTA 2018 Physics | Objective

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Question 1

A radioactive sample of Δₗ decays into Δₘ with a half-life of 5.27 years. If the initial activity of the sample is 2.00 mCi, what is the activity of the sample after 10.5 years?

A. 0.500 mCi

Correct B. 1.00 mCi

C. 1.50 mCi

D. 2.00 mCi

Correct Answer: B

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Question 2

A 2.00 mF capacitor is connected in series with a 3.00 kΩ resistor and a 120 V AC source. If the frequency of the source is 60.0 Hz, what is the impedance of the circuit?

A. 1.50 kΩ

B. 2.00 kΩ

Correct C. 2.50 kΩ

D. 3.00 kΩ

Correct Answer: C

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Question 3

A projectile is launched from the ground with an initial velocity of 20.0 m/s at an angle of 60.0° above the horizontal. If the air resis\tance is negligible, what is the maximum height reached by the projectile?

A. 10.0 m

B. 15.0 m

Correct C. 20.0 m

D. 25.0 m

Correct Answer: C

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Question 4

A gas occupies a volume of 2.00 L at a pressure of 1.00 atm and a temperature of 20.0°C. If the pressure is increased to 2.00 atm and the temperature is increased to 40.0°C, what is the new volume of the gas?

A. 1.00 L

B. 2.00 L

C. 3.00 L

Correct D. 4.00 L

Correct Answer: D

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Question 5

A 5.00 g sample of a gas is collected over water at a temperature of 20.0°C and a pressure of 1.00 atm. If the vapor pressure of water at 20.0°C is 2.00 kPa, what is the partial pressure of the gas?

A. 0.500 atm

Correct B. 1.00 atm

C. 1.50 atm

D. 2.00 atm

Correct Answer: B

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Question 6

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 7

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 0.2 m from its equilibrium position and released from rest, what is the angular frequency of the resulting simple harmonic motion?

A. 5 rad/s

Correct B. 10 rad/s

C. 15 rad/s

D. 20 rad/s

Correct Answer: B

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Question 8

A radioactive sample decays at a rate of 0.05% per hour. If the initial activity is 1000 Bq, what is the activity after 5 hours?

Correct A. 900 Bq

B. 950 Bq

C. 1000 Bq

D. 1050 Bq

Correct Answer: A

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Question 9

A gas is heated from 20°C to 100°C at cons\tant pressure. If the initial volume is 2 L, what is the final volume?

A. 4 L

B. 5 L

Correct C. 6 L

D. 8 L

Correct Answer: C

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Question 10

A light source is placed 2 m away from a convex lens of focal length 0.5 m. If the image is formed 1 m away from the lens, what is the magnification of the lens?

A. 2

B. 3

Correct C. 4

D. 5

Correct Answer: C

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Question 11

A parallel plate capacitor has a capaci\tance of 10 μF and is charged to a potential difference of 12 V. If the dis\tance between the plates is doubled, what is the new capaci\tance?

A. 20 μF

Correct B. 5 μF

C. 10 μF

D. 2.5 μF

Correct Answer: B

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Question 12

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

A. 20°

Correct B. 25°

C. 30°

D. 35°

Correct Answer: B

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Question 13

A 2 kg block is attached to a horizontal, massless spring with a force cons\tant of 100 N/m. The block is displaced by 0.2 m from its equilibrium position and released from rest. What is the angular frequency of the resulting simple harmonic motion?

A. 5 rad/s

Correct B. 10 rad/s

C. 15 rad/s

D. 20 rad/s

Correct Answer: B

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Question 14

A 100 μC point charge is placed at the center of a spherical surface of radius 0.1 m. What is the electric flux through the surface?

A. 10^4 Nm^2/C

B. 10^5 Nm^2/C

Correct C. 10^6 Nm^2/C

D. 10^7 Nm^2/C

Correct Answer: C

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Question 15

A nucleus of mass number 238 and atomic number 92 undergoes \alpha decay. What is the mass number of the resulting nucleus?

Correct A. 234

B. 235

C. 236

D. 237

Correct Answer: A

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Question 16

A 100 Hz AC voltage source is connected to a series RLC circuit with R = 10 Ω, L = 0.1 H, and C = 10 μF. If the circuit is initially at rest, what is the maximum value of the current in the circuit?

A. 1 A

B. 2 A

Correct C. 5 A

D. 10 A

Correct Answer: C

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Question 17

A sound wave with a frequency of 200 Hz has a speed of 340 m/s. What is the wavelength of the sound wave?

Correct A. 1.7 m

B. 1.4 m

C. 1.1 m

D. 0.9 m

Correct Answer: A

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Question 18

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 19

A particle of mass 1 kg is moving in a circular path with a radius of 2 m. If the particle has a speed of 4 m/s, what is the centripetal acceleration?

A. 0.5 m/s^2

B. 1 m/s^2

Correct C. 2 m/s^2

D. 4 m/s^2

Correct Answer: C

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Question 20

A magnetic field of 0.5 T is applied to a current-carrying wire with a length of 1 m. If the current is 2 A, what is the force on the wire?

A. 0.5 N

B. 1 N

Correct C. 2 N

D. 5 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 of the particle?

Correct A. L/2

B. L/4

C. 3L/4

D. L

Correct Answer: A

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Question 22

A circuit consists of a 12 V battery, a 4 Ω resistor, and an inductor of induc\tance 0.5 H. The circuit is connected to a switch that is initially open. At time $t = 0$, the switch is closed. What is the current in the circuit at time $t = 2$ s?

A. 0.5 A

Correct B. 1 A

C. 2 A

D. 4 A

Correct Answer: B

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Question 23

A simple p\endulum of length $L$ and mass $m$ is released from rest at an angle $\theta$ from the vertical. What is the angular frequency of the p\endulum?

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

B. \frac{g}{L}

C. \frac{L}{g}

D. \frac{g}{L^2}

Correct Answer: A

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Question 24

A heat engine operates between two reservoirs at temperatures $T_1 = 500 K$ and $T_2 = 300 K$. The engine has an efficiency of $40%$. What is the temperature of the cold reservoir?

A. 200 K

Correct B. 250 K

C. 300 K

D. 350 K

Correct Answer: B

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Question 25

A vector $\vec{a}$ has a magnitude of $5$ units and makes an angle of $30^\circ$ with the positive $x$-axis. What is the $y$-component of the vector?

Correct A. 2.5

B. 3.5

C. 4.5

D. 5.5

Correct Answer: A

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