Practice post utme unilorin physics 2020 Past Questions

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 $0 < x < \frac{L}{4}$?

Correct A. 0.25

B. 0.5

C. 0.75

D. 1.0

Correct Answer: A

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Question 2

A capacitor consists of two parallel plates, each of area $A$ and separated by a dis\tance $d$. The plates are charged to a potential difference $V$. What is the capaci\tance of the capacitor?

Correct A. \frac{\epsilon_0 A}{d}

B. \frac{\epsilon_0 A}{2d}

C. \frac{2\epsilon_0 A}{d}

D. \frac{\epsilon_0 A}{2d^2}

Correct Answer: A

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Question 3

A beam of light passes through a prism and is re\fracted. The angle of incidence is $30^\circ$ and the angle of re\fraction is $20^\circ$. What is the angle of deviation?

Correct A. 10^\circ

B. 20^\circ

C. 30^\circ

D. 40^\circ

Correct Answer: A

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Question 4

A radioactive sample decays at a rate given by the equation $N(t) = N_0 e^{-\lambda t}$. If the initial number of nuclei is $10^6$ and the decay cons\tant is $\lambda = 0.1$ s$^{-1}$, what is the number of nuclei remaining after $t = 10$ s?

Correct A. 5.0 \times 10^5

B. 1.0 \times 10^6

C. 2.0 \times 10^6

D. 5.0 \times 10^6

Correct Answer: A

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Question 5

A lens of focal length $f$ forms an image of an object at a dis\tance $u$ from the lens. The magnification of the lens is given by the equation $M = \frac{v}{u} = \frac{f}{u - f}$. If the object is placed at a dis\tance $u = 20$ cm from the lens and the focal length is $f = 10$ cm, what is the magnification of the lens?

Correct A. 0.5

B. 1.0

C. 2.0

D. 5.0

Correct Answer: A

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Question 6

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 $L = 2 \times 10^{-3} , \text{kg} cdot \text{m}^2/\text{s}$, what is the particle's speed?

A. $2 \times 10^2 , \text{m/s}$

Correct B. $2 \times 10^3 , \text{m/s}$

C. $2 \times 10^4 , \text{m/s}$

D. $2 \times 10^5 , \text{m/s}

Correct Answer: B

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Question 7

A wave has a frequency of $f = 50 , \text{Hz}$ and a wavelength of $\lambda = 2 , \text{m}$. What is the wave's speed?

A. $100 , \text{m/s}$

Correct B. $200 , \text{m/s}$

C. $500 , \text{m/s}$

D. $1000 , \text{m/s}

Correct Answer: B

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Question 8

A circuit consists of a $10 , \Omega$ resistor, a $20 , \Omega$ resistor, and a $5 , \Omega$ resistor connected in series. What is the total resis\tance of the circuit?

A. $35 , \Omega$

B. $40 , \Omega$

Correct C. $45 , \Omega$

D. $50 , \Omega

Correct Answer: C

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Question 9

A light wave has a frequency of $f = 5 \times 10^{14} , \text{Hz}$ and a wavelength of $\lambda = 600 , \text{nm}$. What is the wave's speed?

Correct A. $3 \times 10^8 , \text{m/s}$

B. $3 \times 10^9 , \text{m/s}$

C. $3 \times 10^{10} , \text{m/s}$

D. $3 \times 10^{11} , \text{m/s}

Correct Answer: A

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Question 10

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 $L = 2 \times 10^{-3} , \text{kg} cdot \text{m}^2/\text{s}$, what is the particle's speed?

A. $2 \times 10^2 , \text{m/s}$

Correct B. $2 \times 10^3 , \text{m/s}$

C. $2 \times 10^4 , \text{m/s}$

D. $2 \times 10^5 , \text{m/s}

Correct Answer: B

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Question 11

A particle of mass 2 kg is moving in a straight line with an initial velocity of 5 m/s. It experiences a force of 10 N due to friction. Assuming the force of friction is cons\tant, calculate the particle's velocity after 4 seconds.

A. 15 m/s

B. 20 m/s

Correct C. 25 m/s

D. 30 m/s

Correct Answer: C

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Question 12

A wave has a frequency of 20 Hz and a wavelength of 0.5 m. Calculate the speed of the wave.

A. 10 m/s

Correct B. 20 m/s

C. 30 m/s

D. 40 m/s

Correct Answer: B

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Question 13

A body is at rest on a horizontal frictionless surface. A cons\tant horizontal force of 10 N is applied to the body. Calculate the acceleration of the body.

A. 1 m/s^2

Correct B. 2 m/s^2

C. 3 m/s^2

D. 4 m/s^2

Correct Answer: B

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Question 14

A block of mass 5 kg is attached to a horizontal 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. Calculate 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 15

A sound wave has a frequency of 200 Hz and a speed of 340 m/s. Calculate the wavelength of the wave.

A. 1.7 m

B. 1.8 m

C. 1.9 m

Correct D. 2.0 m

Correct Answer: D

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Question 16

A radioactive sample of Δₗ emits Δₗπ particles with a half-life of 3.8 days. If 75% of the sample decays in 11.4 days, what is the decay cons\tant λ?

Correct A. 0.0183 day⁻¹²

B. 0.0185 day⁻¹²

C. 0.0187 day⁻¹²

D. 0.0189 day⁻¹²

Correct Answer: A

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Question 17

A convex lens of focal length 15 cm forms an image of a dis\tant object on a screen 30 cm from the lens. What is the magnification of the lens?

A. 0.5

Correct B. 1

C. 1.5

D. 2

Correct Answer: B

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Question 18

A gas at 300 K and 1 atm is compressed to 4 atm. If the volume of the gas is reduced by a factor of 2, what is the new temperature of the gas?

A. 400 K

Correct B. 500 K

C. 600 K

D. 700 K

Correct Answer: B

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Question 19

A circuit consists of a 12 V battery, a 4 Ω resistor, and a 6 Ω resistor connected in series. What is the current in the circuit?

A. 0.5 A

Correct B. 1 A

C. 1.5 A

D. 2 A

Correct Answer: B

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Question 20

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

B. 100 Ω

Correct C. 150 Ω

D. 200 Ω

Correct Answer: C

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Question 21

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

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

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

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

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

Correct Answer: A

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Question 22

A wave of frequency $f$ and wavelength $\lambda$ is traveling through a medium with a speed $v$. If the wave is reflected from a fixed \end, what is the frequency of the reflected wave?

A. f

Correct B. 2f

C. \frac{f}{2}

D. \frac{f}{\lambda}

Correct Answer: B

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Question 23

A circuit consists of a resistor $R$ and an inductor $L$ connected in series. If the circuit is driven by a voltage source $V$ with a frequency $f$, what is the impedance of the circuit?

Correct A. \sqrt{R^2 + $ \omega L $^2}

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

C. \frac{\omega L}{R}

D. \frac{R^2}{\omega L}

Correct Answer: A

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Question 24

A nucleus of mass number $A$ and atomic number $Z$ undergoes \beta decay. If the decay is accompanied by the emission of a neutrino, what is the resulting nucleus?

A. A

B. A-1

Correct C. A+1

D. A-2

Correct Answer: C

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Question 25

A charged particle of mass $m$ and charge $q$ is moving in a magnetic field $B$ with a velocity $v$. If the particle is deflected by an angle $\theta$ from its original path, what is the magnitude of the magnetic force acting on the particle?

Correct A. qvB\sin\theta

B. qvB\cos\theta

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

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

Correct Answer: A

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