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POST UTME BOWEN UNIVERSITY 2018 Physics | Objective

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Question 1

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_1\( x \ $ = \sqrt{\frac{2}{L}} \sinleft$ \frac{pi x}{L}\right $). What is the probability of finding the particle in the region $0 < x < \frac{L}{2}$?

Correct A. \frac{1}{2}

B. \frac{1}{4}

C. \frac{1}{8}

D. \frac{1}{16}

Correct Answer: A

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Question 2

A block of mass $M$ is attached to a horizontal, massless spring with force cons\tant $k$. The block is displaced by a dis\tance $x$ from its equilibrium position and released from rest. Assuming the motion is simple harmonic, what is the angular frequency of the block's 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 3

A \tank is filled with water to a height of $h$. A small hole of area $A$ is made at the bottom of the \tank. Assuming the water flows out of the hole with a speed $v$, what is the rate at which the water level in the \tank falls?

Correct A. \frac{A}{h}v

B. \frac{Ah}{v}

C. \frac{v}{Ah}

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

Correct Answer: A

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Question 4

A particle of mass $m$ is moving in a circular path of radius $r$ with a cons\tant speed $v$. What is the magnitude of the particle's acceleration?

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

B. \frac{rv^2}{m}

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

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

Correct Answer: A

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Question 5

A block of mass $M$ is placed on a frictionless surface and a force $F$ is applied to it. The block accelerates with a cons\tant acceleration $a$. What is the magnitude of the force $F$?

Correct A. Ma

B. \frac{Ma}{2}

C. \frac{2Ma}{3}

D. \frac{3Ma}{4}

Correct Answer: A

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Question 6

A particle of mass m is attached to a spring with spring cons\tant k. The particle is displaced from its equilibrium position by a dis\tance x and released from rest. Assuming the motion is simple harmonic, find the angular frequency ω in terms of k and m.

A. \omega = \frac{k}{m}

B. \omega = \sqrt{\frac{m}{k}}

C. \omega = \frac{m}{k}

Correct D. \omega = \sqrt{\frac{k}{m}}

Correct Answer: D

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Question 7

A wave of wavelength λ and frequency f is traveling through a medium with speed v. Find the wave number k in terms of λ and f.

A. k = \frac{\lambda}{2\pi}

Correct B. k = \frac{2\pi}{\lambda}

C. k = \frac{\lambda}{f}

D. k = \frac{f}{\lambda}

Correct Answer: B

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Question 8

A radioactive sample decays with a half-life of t1/2. Find the activity A(t) at time t in terms of the initial activity A0.

A. A(t) = A0 e^{\frac{t}{t_{1/2}}}

Correct B. A(t) = A0 e^{-\frac{t}{t_{1/2}}}

C. A(t) = A0 e^{\frac{t_{1/2}}{t}}

D. A(t) = A0 e^{-\frac{t_{1/2}}{t}}

Correct Answer: B

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Question 9

A gas is heated from 0°C to 100°C at cons\tant volume. Find the change in internal energy ΔU in terms of the specific heat capacity c.

A. \Delta U = mc\frac{\Delta T}{2}

Correct B. \Delta U = mc\Delta T

C. \Delta U = mc\frac{\Delta T}{3}

D. \Delta U = mc\frac{\Delta T}{4}

Correct Answer: B

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Question 10

A circuit consists of a resistor R and an inductor L in series. Find the impedance Z in terms of R and L.

A. Z = R + \omega L

B. Z = \sqrt{R^2 - $ \omega L $^2}

Correct C. Z = \sqrt{R^2 + $ \omega L $^2}

D. Z = R - \omega L

Correct Answer: C

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Question 11

A parallel plate capacitor has plates of area 0.04 m^2 and separation 0.02 m. If a potential difference of 10 V is applied across the plates, calculate the capaci\tance.

A. 2.5 x 10^-10 F

Correct B. 5.0 x 10^-10 F

C. 1.0 x 10^-9 F

D. 2.0 x 10^-9 F

Correct Answer: B

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Question 12

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

Correct A. 20°

B. 30°

C. 40°

D. 50°

Correct Answer: A

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Question 13

A circuit consists of a 10 Ω resistor, a 20 Ω resistor, and a 5 Ω resistor connected in series. If a voltage of 12 V is applied across the circuit, calculate the current through the 5 Ω resistor.

A. 0.4 A

B. 0.6 A

Correct C. 0.8 A

D. 1.0 A

Correct Answer: C

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Question 14

A sound wave has a frequency of 200 Hz and a wavelength of 0.5 m. Calculate the speed of the sound wave.

A. 100 m/s

Correct B. 200 m/s

C. 300 m/s

D. 400 m/s

Correct Answer: B

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Question 15

A heat engine operates between a temperature of 500 K and a temperature of 300 K. Calculate the efficiency of the engine.

A. 0.25

B. 0.33

Correct C. 0.40

D. 0.50

Correct Answer: C

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Question 16

A block of mass 2 kg is attached to a horizontal, massless spring with a spring cons\tant of 100 N/m. The block is displaced by 0.2 m from its equilibrium position and released from rest. Assuming the block undergoes simple harmonic motion, calculate the maximum speed of the block as it passes through the equilibrium position.

A. 4 m/s

Correct B. 6 m/s

C. 8 m/s

D. 10 m/s

Correct Answer: B

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Question 17

A particle of mass 0.5 kg is moving in a circular path of radius 2 m with a cons\tant speed of 4 m/s. If the particle is subjected to a centripetal acceleration of 2 m/s^2, calculate the force exerted on the particle.

A. 2 N

B. 4 N

Correct C. 6 N

D. 8 N

Correct Answer: C

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Question 18

A parallel plate capacitor consists of two plates, each of area 0.1 m^2, separated by a dis\tance of 0.01 m. If the capaci\tance of the capacitor is 10^-6 F, calculate the charge stored on the capacitor when a potential difference of 10 V is applied across it.

A. 10^-8 C

B. 10^-7 C

Correct C. 10^-6 C

D. 10^-5 C

Correct Answer: C

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Question 19

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%, calculate 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 20

A projectile is launched from the ground with an initial velocity of 20 m/s at an angle of 60 degrees above the horizontal. If the projectile lands 10 m away from the point of launch, calculate the time of flight.

A. 2 s

B. 3 s

Correct C. 4 s

D. 5 s

Correct Answer: C

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Question 21

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 of the particle?

A. 16 m/s^2

B. 32 m/s^2

Correct C. 48 m/s^2

D. 64 m/s^2

Correct Answer: C

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Question 22

A 10 μF capacitor is connected in series with a 20 Ω resistor and a 5 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 23

A gas at a pressure of 2 atm and a volume of 10 L expands to a volume of 20 L. What is the final pressure of the gas?

A. 1 atm

B. 2 atm

Correct C. 3 atm

D. 4 atm

Correct Answer: C

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Question 24

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

B. 15 m

Correct C. 20 m

D. 25 m

Correct Answer: C

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Question 25

A 100 Ω resistor is connected in parallel with a 200 Ω resistor. What is the equivalent resis\tance of the circuit?

A. 50 Ω

Correct B. 75 Ω

C. 100 Ω

D. 150 Ω

Correct Answer: B

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