POST UTME PAN-ATLANTIC UNIVERSITY 2021 Physics | Objective

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Question 1 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 angle between the velocity vector and the radius vector at the ins\tant when the particle is at the top of its circular path?
A. 0°
B. 30°
Correct C. 45°
D. 60°

Correct Answer: C

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Question 2 View Details
A wave has a frequency of 50 Hz and a wavelength of 0.2 m. If the wave is traveling in the positive x-direction, what is the direction of the group velocity?
Correct A. Positive x-direction
B. Negative x-direction
C. Positive y-direction
D. Negative y-direction

Correct Answer: A

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Question 3 View Details
A block of mass 5 kg is moving down a frictionless inclined plane with an acceleration of 2 m/s². If the angle of the incline is 30°, what is the force of gravity acting on the block?
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 circuit consists of a 12 V battery, a 4 Ω resistor, and a 6 Ω resistor connected in series. If the current in the circuit is 2 A, what is the potential difference across the 6 Ω resistor?
A. 6 V
Correct B. 8 V
C. 10 V
D. 12 V

Correct Answer: B

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Question 5 View Details
A wave has a frequency of 200 Hz and a wavelength of 0.05 m. If the wave is traveling in the positive x-direction, what is the speed of the wave?
A. 10 m/s
B. 20 m/s
Correct C. 30 m/s
D. 40 m/s

Correct Answer: C

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Question 6 View Details
A parallel plate capacitor has plates of area $A$ and separation $d$. If the capaci\tance is $C$, find the value of the dielectric cons\tant $K$.
A. \( K = \frac{Cd}{A \epsilon_0} \)
B. \( K = \frac{A \epsilon_0}{Cd} \)
Correct C. \( K = \frac{Cd}{A \epsilon_0} \)
D. \( K = \frac{A \epsilon_0}{Cd} \)

Correct Answer: C

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Question 7 View Details
A light ray passes through a prism of angle $A$ and is re\fracted at an angle $B$. If the angle of deviation is $D$, find the value of the re\fractive index $n$.
A. \( n = \frac{\sin \left\( \frac{A}{2} \right \)}{\sin \left\( \frac{D}{2} \right \)} \)
Correct B. \( n = \frac{\sin \left\( \frac{D}{2} \right \)}{\sin \left\( \frac{A}{2} \right \)} \)
C. \( n = \frac{\sin \left\( \frac{A}{2} \right \)}{\sin \left\( \frac{D}{2} \right \)} \)
D. \( n = \frac{\sin \left\( \frac{D}{2} \right \)}{\sin \left\( \frac{A}{2} \right \)} \)

Correct Answer: B

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Question 8 View Details
A particle of mass $m$ is moving in a circular orbit of radius $r$ with a speed $v$. If the centripetal force is $F_c$, find the value of the angular momentum $L$.
A. \( L = \frac{F_c r^2}{mv} \)
B. \( L = \frac{mv}{F_c r} \)
Correct C. \( L = mvr \)
D. \( L = \frac{mv}{rF_c} \)

Correct Answer: C

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Question 9 View Details
A wave of wavelength $\lambda$ and frequency $f$ is traveling through a medium of speed $v$. If the wave is reflected at a surface, find the value of the reflected wave's frequency $f_r$.
A. \( f_r = \frac{f}{2} \)
Correct B. \( f_r = 2f \)
C. \( f_r = \frac{f}{4} \)
D. \( f_r = 4f \)

Correct Answer: B

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Question 10 View Details
A particle of mass $m$ is moving in a straight line with a velocity $v$. If the particle is subject to a force $F$, find the value of the acceleration $a$.
A. \( a = \frac{mv}{F} \)
B. \( a = \frac{F}{mv} \)
Correct C. \( a = \frac{F}{m} \)
D. \( a = \frac{mv}{F} \)

Correct Answer: C

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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. 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 12 View Details
A 10 μF capacitor is connected in series with a 20 Ω resistor and a 100 V battery. What is the current flowing through the circuit?
A. 0.5 A
Correct B. 1 A
C. 2 A
D. 5 A

Correct Answer: B

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Question 13 View Details
A wave function is given by ψ(x) = Ae^(ikx). What is the wavelength of the wave?
Correct A. 2π
B. 4π
C. 6π
D. 8π

Correct Answer: A

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Question 14 View Details
A block of mass 5 kg is placed on a frictionless surface. A force of 10 N is applied to the block, cau\sing it to accelerate at 2 m/s^2. What is the normal force exerted on the block?
A. 10 N
B. 20 N
Correct C. 30 N
D. 40 N

Correct Answer: C

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Question 15 View Details
A projectile is launched at an angle of 60° above the horizontal with an initial velocity of 20 m/s. What is the maximum height reached by the projectile?
A. 10 m
Correct B. 20 m
C. 30 m
D. 40 m

Correct Answer: B

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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 force?
A. 10 N
Correct B. 12 N
C. 15 N
D. 20 N

Correct Answer: B

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Question 17 View Details
A beam 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 18 View Details
A radioactive sample has a half-life of 5 years. If the initial activity is 100 Bq, what is the activity after 10 years?
A. 20 Bq
B. 25 Bq
C. 30 Bq
Correct D. 40 Bq

Correct Answer: D

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Question 19 View Details
A particle of mass 1 kg is moving in a straight line with a velocity of 5 m/s. If a force of 2 N is applied to the particle, what is the acceleration?
A. 0.5 m/s²
B. 1 m/s²
Correct C. 2 m/s²
D. 5 m/s²

Correct Answer: C

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Question 20 View Details
A lens of focal length 10 cm is used to form an image of an object at a dis\tance of 20 cm. What is the magnification?
A. -0.5
Correct B. -1
C. -2
D. -5

Correct Answer: B

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Question 21 View Details
A particle of mass $m$ is moving in a circular path of radius $r$ with a cons\tant speed $v$. The particle experiences a centripetal force $F_c$ given by $F_c = \frac{mv^2}{r}$. If the particle's speed is doubled to $2v$, what is the new centripetal force $F_{c,new}$?
Correct A. \frac{4mv^2}{r}
B. \frac{2mv^2}{r}
C. \frac{mv^2}{2r}
D. \frac{mv^2}{4r}

Correct Answer: A

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Question 22 View Details
A parallel plate capacitor consists of two plates of area $A$ separated by a dis\tance $d$. The plates are charged with a charge $Q$ on each plate. If the dis\tance between the plates is doubled to $2d$, what is the new capaci\tance $C_{new}$?
A. \frac{Q}{V}
B. \frac{2Q}{V}
Correct C. \frac{Q}{2V}
D. \frac{Q}{4V}

Correct Answer: C

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Question 23 View Details
A circuit consists of a resistor $R$ and an inductor $L$ connected in series. The circuit is driven by a voltage source $V$ with a frequency $f$. If the induc\tance is doubled to $2L$, what is the new inductive reac\tance $X_{L,new}$?
Correct A. \omega 2L
B. \omega L
C. \frac{\omega L}{2}
D. \frac{\omega L}{4}

Correct Answer: A

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Question 24 View Details
A gas is confined to a cylinder of volume $V$ with a piston of mass $m$ at the bottom. The gas is heated, cau\sing the piston to rise. If the initial pressure is $P_0$ and the final pressure is $P_f$, what is the new volume $V_{new}$?
A. \frac{P_f V}{P_0}
Correct B. \frac{P_0 V}{P_f}
C. \frac{P_0 V}{2P_f}
D. \frac{2P_0 V}{P_f}

Correct Answer: B

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Question 25 View Details
A spring with a spring cons\tant $k$ is stretched by a dis\tance $x$. If the spring cons\tant is doubled to $2k$, what is the new force $F_{new}$?
Correct A. 2kx
B. kx
C. \frac{kx}{2}
D. \frac{kx}{4}

Correct Answer: A

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