Practice post utme caleb university physics 2019 Past Questions

Question 1

A radioactive sample of Uranium-238 undergoes \alpha decay. If the half-life of Uranium-238 is 4.5 billion years, what is the decay cons\tant (λ) in s^-1?

Correct A. 1.54\times 10^{-18} s^-1

B. 1.54\times 10^{-17} s^-1

C. 1.54\times 10^{-16} s^-1

D. 1.54\times 10^{-15} s^-1

Correct Answer: A

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Question 2

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. What is the magnitude of the net 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 3

A convex lens of focal length 20 cm is placed in contact with a concave lens of focal length -15 cm. What is the focal length of the combination?

A. -5 cm

B. -10 cm

C. -15 cm

Correct D. -20 cm

Correct Answer: D

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Question 4

A light ray is incident on a plane mirror at an angle of 30°. What is the angle of reflection?

A. 15°

Correct B. 30°

C. 45°

D. 60°

Correct Answer: B

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Question 5

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

A. 1.57 rad/s

B. 3.14 rad/s

Correct C. 6.28 rad/s

D. 9.42 rad/s

Correct Answer: C

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Question 6

A gas at $25^{circ}C$ and $1.0 \times 10^5 , Pa$ is heated to $50^{circ}C$ while maintaining cons\tant pressure. What is the new volume of the gas?

A. $ 1.33 , m^3 $

Correct B. $ 1.67 , m^3 $

C. $ 2.00 , m^3 $

D. $ 2.33 , m^3 $

Correct Answer: B

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Question 7

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 magnetic field of strength $B$, what is the magnitude of the magnetic force acting on it?

Correct A. $ \frac{m v^2}{r} $

B. $ \frac{m v^2}{r} \sin \theta $

C. $ \frac{m v^2}{r} \cos \theta $

D. $ \frac{m v^2}{r} \tan \theta $

Correct Answer: A

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Question 8

A circuit consists of a $10 , Omega$ resistor, a $5 , Omega$ resistor, and a $20 , Omega$ resistor connected in series. If a voltage of $12 , V$ is applied across the circuit, what is the current flowing through the $10 , Omega$ resistor?

A. ( 0.4 , A )

Correct B. ( 0.6 , A )

C. ( 0.8 , A )

D. ( 1.0 , A )

Correct Answer: B

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Question 9

A wave has a frequency of $50 , Hz$ and a wavelength of $10 , m$. What is the speed of the wave?

A. $ 500 , m/s $

Correct B. $ 1000 , m/s $

C. $ 1500 , m/s $

D. $ 2000 , m/s $

Correct Answer: B

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Question 10

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 magnetic field of strength $B$, what is the magnitude of the magnetic force acting on it?

Correct A. $ \frac{m v^2}{r} $

B. $ \frac{m v^2}{r} \sin \theta $

C. $ \frac{m v^2}{r} \cos \theta $

D. $ \frac{m v^2}{r} \tan \theta $

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 acceleration of 2 m/s^2, what is the magnitude of the net force acting on the particle?

A. 8 N

B. 12 N

Correct C. 16 N

D. 20 N

Correct Answer: C

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Question 12

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

A heat engine operates between two reservoirs at temperatures 500 K and 300 K. If the engine absorbs 1000 J of heat from the high-temperature reservoir, what is the efficiency of the engine?

A. 0.25

Correct B. 0.33

C. 0.5

D. 0.67

Correct Answer: B

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Question 14

A magnetic field of magnitude 0.5 T is directed perp\endicular to the plane of a circular loop of radius 0.2 m. If the loop carries a current of 2 A, what is the magnitude of the magnetic moment of the loop?

A. 0.2 A m^2

Correct B. 0.4 A m^2

C. 0.6 A m^2

D. 0.8 A m^2

Correct Answer: B

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Question 15

A sound wave with frequency 200 Hz and amplitude 0.1 m is traveling through a medium with speed 340 m/s. If the wave is reflected from a rigid boundary, what is the amplitude of the reflected wave?

Correct A. 0.05 m

B. 0.1 m

C. 0.15 m

D. 0.2 m

Correct Answer: A

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Question 16

A particle of mass 2 kg is projected from the origin with an initial velocity of 20 m/s at an angle of 60° to the horizontal. If the acceleration due to gravity is 9.8 m/s², calculate the time taken by the particle to reach its maximum height.

Correct A. 2 s

B. 3 s

C. 4 s

D. 5 s

Correct Answer: A

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Question 17

A radioactive subs\tance has a half-life of 5 years. If 100 g of the subs\tance is initially present, how much of the subs\tance will remain after 10 years?

Correct A. 25 g

B. 50 g

C. 75 g

D. 100 g

Correct Answer: A

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Question 18

A gas at a pressure of 2 atm and a temperature of 300 K is allowed to expand to a volume of 5 m³. If the gas is ideal and the expansion is isothermal, what is the final pressure of the gas?

A. 1 atm

Correct B. 1.5 atm

C. 2 atm

D. 2.5 atm

Correct Answer: B

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Question 19

A body of mass 10 kg is at rest on a horizontal surface. A horizontal force of 20 N is applied to the body. If the coefficient of static friction between the body and the surface is 0.5, what is the acceleration of the body?

A. 2 m/s²

B. 4 m/s²

Correct C. 6 m/s²

D. 8 m/s²

Correct Answer: C

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Question 20

A liquid of density 1000 kg/m³ is poured into a container of height 2 m. If the pressure at the bottom of the container is 100 kPa, what is the pressure at the top of the container?

Correct A. 50 kPa

B. 75 kPa

C. 100 kPa

D. 125 kPa

Correct Answer: A

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Question 21

A parallel plate capacitor consists of two plates of area $A$ separated by a dis\tance $d$. The capaci\tance is given by $C=\frac{varepsilon_0 A}{d}$. If the area of the plates is doubled and the dis\tance between them is halved, what is the new capaci\tance?

Correct A. \frac{4 varepsilon_0 A}{d}

B. \frac{2 varepsilon_0 A}{d}

C. \frac{\varepsilon_0 A}{2d}

D. \frac{\varepsilon_0 A}{d}

Correct Answer: A

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Question 22

A particle of mass $m$ is moving in a circular path of radius $r$ with a cons\tant speed $v$. The force acting on the particle is given by $F=\frac{mv^2}{r}$. If the speed of the particle is doubled, what is the new force?

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

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

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

Correct D. \frac{4mv^2}{r}

Correct Answer: D

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Question 23

A light ray passes from air into a glass slab of thickness $t$ and re\fractive index $\mu$. The angle of incidence is $\theta_i$. What is the angle of re\fraction?

Correct A. \sin^{-1}\left$ \frac{\mu \sin \theta_i}{1+\mu \sin \theta_i}\right $

B. \sin^{-1}\left$ \frac{\sin \theta_i}{\mu}\right $

C. \sin^{-1}\left$ \frac{\sin \theta_i}{1+\mu}\right $

D. \sin^{-1}\left$ \frac{\mu \sin \theta_i}{1-\mu \sin \theta_i}\right $

Correct Answer: A

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Question 24

A circuit consists of a resistor $R$ and an inductor $L$ connected in series. The current through the circuit is given by $I=\frac{V}{R+L\omega}$, where $V$ is the voltage and $\omega$ is the angular frequency. If the voltage is doubled and the angular frequency is halved, what is the new current?

A. \frac{2V}{R+L\omega}

B. \frac{V}{R+L\omega}

C. \frac{V}{R+2L\omega}

Correct D. \frac{2V}{R+2L\omega}

Correct Answer: D

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Question 25

A wave function $\psi(x)$ is given by $\psi(x)=Ae^{ikx}$, where $A$ is a cons\tant and $k$ is the wave number. What is the probability density of the wave function?

Correct A. |A|^2

B. A^2

C. A^2e^{-2ikx}

D. A^2e^{2ikx}

Correct Answer: A

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