Practice Post UTME LAUTECH physics 2018 Past Questions

Question 1

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 subject 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 2

A radioactive sample has a half-life of 5 years. If the initial activity of the sample is 1000 Bq, what is the activity of the sample after 10 years?

Correct A. 125 Bq

B. 250 Bq

C. 500 Bq

D. 1000 Bq

Correct Answer: A

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Question 3

A magnetic field of 0.5 T is applied to a coil of 100 turns and a radius of 0.2 m. If the current in the coil is 2 A, what is the magnitude of the torque experienced by the coil?

A. 0.1 Nm

Correct B. 0.2 Nm

C. 0.3 Nm

D. 0.4 Nm

Correct Answer: B

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Question 4

A block of mass 5 kg is attached to a spring with a spring cons\tant of 200 N/m. If the block is displaced by 0.2 m from its equilibrium position and released, what is the magnitude of the acceleration of the block?

A. 2 m/s^2

Correct B. 4 m/s^2

C. 6 m/s^2

D. 8 m/s^2

Correct Answer: B

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Question 5

A particle of mass 3 kg is moving in a circular path of radius 2 m with a cons\tant speed of 3 m/s. If the particle is subject to a centripetal force of 15 N, what is the magnitude of the acceleration of the particle?

A. 10 m/s^2

B. 12 m/s^2

Correct C. 15 m/s^2

D. 20 m/s^2

Correct Answer: C

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Question 6

A uniform magnetic field of magnitude 2 T is directed along the z-axis. A current of 5 A flows through a wire loop of radius 0.1 m, placed in the x-y plane. What is the magnitude of the magnetic moment of the loop?

A. 0.01 A m^2

Correct B. 0.1 A m^2

C. 1 A m^2

D. 10 A m^2

Correct Answer: B

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Question 7

A sound wave with frequency 200 Hz and amplitude 0.1 m is traveling through a medium with speed 340 m/s. What is the wavelength of the wave?

Correct A. 1.7 m

B. 1.7 cm

C. 17 m

D. 17 cm

Correct Answer: A

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Question 8

A gas is heated from 300 K to 400 K at cons\tant volume. What is the change in internal energy of the gas?

Correct A. 100 J

B. 1000 J

C. 10000 J

D. 100000 J

Correct Answer: A

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Question 9

A particle is projected at an angle of 60° to the horizontal with initial velocity 20 m/s. What is the time of flight of the particle?

A. 1 s

Correct B. 2 s

C. 3 s

D. 4 s

Correct Answer: B

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Question 10

A vector A has magnitude 5 m and direction 30° to the x-axis. What is the magnitude of the vector B such that the resul\tant vector C is 10 m at an angle of 60° to the x-axis?

A. 5 m

B. 10 m

Correct C. 15 m

D. 20 m

Correct Answer: C

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

A. 0.1 s

Correct B. 0.2 s

C. 0.5 s

D. 1 s

Correct Answer: B

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Question 13

A wave function is given by ψ(x) = Ae^$ -αx^2 $. What is the value of α if the wave function is normalized?

Correct A. 1/2

B. 1/4

C. 1/8

D. 1/16

Correct Answer: A

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Question 14

A simple harmonic motion is given by x(t) = 2 \sin$ 3t + π/4 $. What is the angular frequency of the motion?

Correct A. 3 rad/s

B. 4 rad/s

C. 5 rad/s

D. 6 rad/s

Correct Answer: A

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Question 15

A circuit consists of a 10 Ω resistor, a 20 Ω resistor, and a 5 Ω resistor connected in parallel. What is the equivalent resis\tance of the circuit?

A. 5 Ω

B. 10 Ω

Correct C. 15 Ω

D. 20 Ω

Correct Answer: C

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Question 16

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 experiences a centripetal acceleration of 2 m/s², what is the magnitude of the net force acting on the particle?

A. 10 N

Correct B. 12 N

C. 15 N

D. 18 N

Correct Answer: B

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Question 17

A parallel plate capacitor has a capaci\tance of 5 μF and is charged to a potential difference of 10 V. If the dis\tance between the plates is doubled, what is the new capaci\tance?

Correct A. 2.5 μF

B. 5 μF

C. 10 μF

D. 20 μF

Correct Answer: A

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Question 18

A block of mass 5 kg is placed on a frictionless surface and is given an initial velocity of 2 m/s. If the block experiences a cons\tant acceleration of 1 m/s², what is the time it takes for the block to reach a velocity of 5 m/s?

A. 2 s

Correct B. 3 s

C. 4 s

D. 5 s

Correct Answer: B

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Question 19

A circuit consists of a 10 Ω resistor, a 20 Ω resistor, and a 5 Ω resistor connected in series. If a voltage of 15 V is applied across the circuit, what is the current flowing through the 5 Ω resistor?

A. 0.5 A

B. 1 A

Correct C. 1.5 A

D. 2 A

Correct Answer: C

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Question 20

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

A. 10°

Correct B. 20°

C. 30°

D. 40°

Correct Answer: B

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Question 21

A particle of mass $m$ is moving in a circular orbit of radius $r$ under the influence of a central force given by $F(r) = -\frac{k}{r^2}$. If the particle's angular momentum is $L = 2mvr$, find the total energy of the particle.

A. $\frac{1}{2}mv^2 + \frac{k}{r}$

Correct B. $\frac{1}{2}mv^2 - \frac{k}{r}$

C. $-\frac{1}{2}mv^2 - \frac{k}{r}$

D. $-\frac{1}{2}mv^2 + \frac{k}{r}$

Correct Answer: B

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Question 22

A wave of frequency $f$ is traveling through a medium with speed $v$. If the wave's amplitude is $A$, find the intensity of the wave.

Correct A. $\frac{1}{2}\rho\omega^2A^2v$

B. $\frac{1}{2}\rho\omega^2A^2v^2$

C. $\frac{1}{2}\rho\omega^2A^2$

D. $\frac{1}{2}\rho\omega^2A^2v^3$

Correct Answer: A

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Question 23

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

Correct A. $\frac{1}{2}kx^2$

B. $\frac{1}{2}mx^2$

C. $\frac{1}{2}kx^4$

D. $\frac{1}{2}mx^4$

Correct Answer: A

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Question 24

A radioactive sample has a half-life of $T_{1/2}$. If the initial activity of the sample is $A_0$, find the activity of the sample after a time $t$.

Correct A. $A_0\left$ \frac{1}{2}\right $^{t/T_{1/2}}$

B. $A_0\left$ \frac{1}{2}\right $^{T_{1/2}/t}$

C. $A_0\left$ \frac{1}{2}\right $^{t/T_{1/2}} + A_0$

D. $A_0\left$ \frac{1}{2}\right $^{t/T_{1/2}} - A_0$

Correct Answer: A

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Question 25

A particle of mass $m$ is moving in a circular orbit of radius $r$ under the influence of a central force given by $F(r) = -\frac{k}{r^2}$. If the particle's angular momentum is $L = 2mvr$, find the total energy of the particle.

A. $\frac{1}{2}mv^2 + \frac{k}{r}$

Correct B. $\frac{1}{2}mv^2 - \frac{k}{r}$

C. $-\frac{1}{2}mv^2 - \frac{k}{r}$

D. $-\frac{1}{2}mv^2 + \frac{k}{r}$

Correct Answer: B

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