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POST UTME VERITAS UNIVERSITY 2019 Physics | Objective

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Question 1

A particle of mass $m$ is moving in a circular path of radius $r$ with a cons\tant speed $v$. If the particle experiences a centripetal force $F_c = \frac{mv^2}{r}$, what is the magnitude of the acceleration of the particle?

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

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

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

D. \frac{v^2}{r^2}

Correct Answer: C

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Question 2

A circuit consists of a 12 V battery, a 4 Ω resistor, and a 6 Ω resistor connected in series. If the circuit is closed, what is the current flowing through the 6 Ω resistor?

A. 1 A

Correct B. 2 A

C. 3 A

D. 4 A

Correct Answer: B

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Question 3

A radioactive sample decays at a rate given by the equation $N(t) = N_0 e^{-kt}$, where $N(t)$ is the number of nuclei remaining at time $t$, $N_0$ is the initial number of nuclei, and $k$ is the decay cons\tant. If the half-life of the sample is 10 minutes, what is the value of $k$?

A. 0.0693 min^{-1}

B. 0.0693 h^{-1}

Correct C. 0.693 min^{-1}

D. 0.693 h^{-1}

Correct Answer: C

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Question 4

A wave function for a particle in a one-dimensional box is given by the equation $\psi(x) = A \sin \left$ \frac{n \pi x}{L} \right $$, where $A$ is a cons\tant, $n$ is an integer, and $L$ is the length of the box. If the particle is in the ground state $ $n = 1$ $, what is the probability of finding the particle in the region $0 < x < L/2$?

A. 1/2

Correct B. 1/4

C. 3/4

D. 1/4

Correct Answer: B

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Question 5

A circuit consists of a 12 V battery, a 4 Ω resistor, and a 6 Ω resistor connected in parallel. If the circuit is closed, what is the current flowing through the 4 Ω resistor?

Correct A. 1 A

B. 2 A

C. 3 A

D. 4 A

Correct Answer: A

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Question 6

A ray of light 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. 40°

B. 50°

Correct C. 60°

D. 70°

Correct Answer: C

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Question 7

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 centripetal acceleration?

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 8

A car is traveling at a speed of 25 m/s. If the driver applies the brakes and the car comes to rest in 4 seconds, what is the magnitude of the deceleration?

A. 5 m/s²

B. 10 m/s²

C. 15 m/s²

Correct D. 20 m/s²

Correct Answer: D

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Question 9

A block of mass 5 kg is attached to a horizontal spring with a force cons\tant of 200 N/m. If the block is displaced by 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 10

A heat engine operates between a high-temperature reservoir at 500 K and a low-temperature reservoir at 300 K. If the engine produces 100 J of work per cycle, what is the efficiency of the engine?

A. 20%

B. 30%

Correct C. 40%

D. 50%

Correct Answer: C

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Question 11

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

A. 0.1 A m^2

B. 0.2 A m^2

Correct C. 0.5 A m^2

D. 1 A m^2

Correct Answer: C

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Question 12

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 force acting on the particle?

A. 10 N

Correct B. 20 N

C. 30 N

D. 40 N

Correct Answer: B

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Question 13

A heat engine operates between two temperatures of 500 K and 300 K. If the efficiency of the engine is 30%, what is the work done by the engine per cycle?

A. 100 J

B. 200 J

Correct C. 300 J

D. 400 J

Correct Answer: C

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Question 14

A 100 Ω resistor is connected in series with a 20 Ω resistor and a 50 Ω resistor. What is the equivalent resis\tance of the circuit?

A. 20 Ω

B. 30 Ω

Correct C. 40 Ω

D. 50 Ω

Correct Answer: C

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Question 15

A block of mass 5 kg is placed on a horizontal surface. If the coefficient of static friction between the block and the surface is 0.5, what is the maximum force that can be applied to the block without cau\sing it to move?

A. 10 N

B. 20 N

Correct C. 25 N

D. 30 N

Correct Answer: C

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Question 16

A gas at 300 K is heated to 400 K. If the initial volume is 2.5 L, what is the final volume, assuming the gas obeys Charles' Law?

A. 3.125 L

Correct B. 4.0 L

C. 5.0 L

D. 6.25 L

Correct Answer: B

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Question 17

A 10 Ω resistor is connected in series with a 20 Ω resistor and a 30 Ω resistor. What is the equivalent resis\tance?

A. 10 Ω

B. 20 Ω

C. 30 Ω

Correct D. 60 Ω

Correct Answer: D

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Question 18

A charged particle moves through a uniform magnetic field. If the particle's velocity is perp\endicular to the magnetic field, what is the direction of the force exerted on the particle?

A. East

Correct B. West

C. North

D. South

Correct Answer: B

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Question 19

A 2 kg block is attached to a horizontal, massless spring with a force cons\tant of 100 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. 0.5 m/s

Correct B. 1.0 m/s

C. 1.5 m/s

D. 2.0 m/s

Correct Answer: B

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Question 20

A heat engine operates between a high-temperature reservoir at 500 K and a low-temperature reservoir at 300 K. If the engine has an efficiency of 30%, what is the temperature of the high-temperature reservoir?

A. 400 K

B. 500 K

Correct C. 600 K

D. 700 K

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 ground state wave function of the particle is given by $psi_0(x) = \sqrt{\frac{2}{L}} \sinleft$ \frac{pi x}{L}\right $$. What is the probability of finding the particle in the region $0 < x < \frac{L}{2}$?

A. 0

Correct B. \frac{1}{2}

C. \frac{2}{3}

D. 1

Correct Answer: B

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Question 22

A block of mass $M$ is placed on a frictionless surface and connected to a horizontal spring with spring cons\tant $k$. The block is displaced by a dis\tance $x$ from its equilibrium position and released from rest. What is the angular frequency of the resulting simple harmonic motion?

Correct A. \sqrt{\frac{k}{M}}

B. \frac{k}{M}

C. \frac{M}{k}

D. \frac{1}{\sqrt{kM}}

Correct Answer: A

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Question 23

A gas of $N$ molecules is confined to a container of volume $V$. The molecules are assumed to be non-interacting and have a mass $m$. The temperature of the gas is $T$. What is the average kinetic energy of the molecules?

Correct A. \frac{3}{2} k_B T

B. \frac{1}{2} k_B T

C. \frac{1}{3} k_B T

D. \frac{2}{3} k_B T

Correct Answer: A

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Question 24

A light wave with wavelength $\lambda$ and frequency $f$ is incident on a double-slit apparatus. The slits are separated by a dis\tance $d$ and the screen is placed a dis\tance $L$ away from the slits. What is the angle of the first minimum in the interference pattern?

Correct A. \frac{\lambda}{d}

B. \frac{d}{\lambda}

C. \frac{2\lambda}{d}

D. \frac{d}{2\lambda}

Correct Answer: A

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Question 25

A circuit consists of a resistor $R$, an inductor $L$, and a capacitor $C$ connected in series. The circuit is driven by an AC voltage source with a frequency $f$. What is the impedance of the circuit?

Correct A. \sqrt{R^2 + $ \omega L - \frac{1}{\omega C} $^2}

B. R + L + C

C. R - L + C

D. R + L - C

Correct Answer: A

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