Practice Post UTME UNIBEN physics 2018 Past Questions

Question 1

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 speed is $v$, what is its angular momentum?

Correct A. mvr

B. mvr^2

C. mv^2r

D. mv^2/r

Correct Answer: A

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Question 2

A block of mass $M$ is placed on a frictionless surface and attached to a horizontal spring with spring cons\tant $k$. If the block is displaced by a dis\tance $x$ and released from rest, what is its maximum speed?

Correct A. \sqrt{kx^2/M}

B. \sqrt{kx^2/M}

C. \sqrt{kx^2/M}

D. \sqrt{kx^2/M}

Correct Answer: A

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Question 3

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

Correct A. f

B. 2f

C. f/2

D. f/\lambda

Correct Answer: A

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Question 4

A radioactive sample has a half-life of $t_{1/2}$. If the initial activity is $A_0$, what is the activity after a time $t$?

Correct A. A_0 e^{-\lambda t}

B. A_0 e^{\lambda t}

C. A_0 + \lambda t

D. A_0 - \lambda t

Correct Answer: A

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Question 5

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 speed is $v$, what is its angular momentum?

Correct A. mvr

B. mvr^2

C. mv^2r

D. mv^2/r

Correct Answer: A

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Question 6

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 force acting on the particle?

A. 8 N

B. 10 N

Correct C. 12 N

D. 16 N

Correct Answer: C

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Question 7

A light ray passes through a prism of angle 30° and is re\fracted at an angle of 20°. If the angle of incidence is 40°, what is the angle of emergence?

A. 60°

B. 70°

Correct C. 80°

D. 90°

Correct Answer: C

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Question 8

A thermodynamic system undergoes a process from state A to state B, where the temperature increases from 20°C to 40°C. If the heat capacity of the system is 100 J/K, what is the change in internal energy?

A. 2000 J

B. 3000 J

Correct C. 4000 J

D. 5000 J

Correct Answer: C

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Question 9

A magnetic field of strength 0.5 T is applied to a current-carrying wire of length 2 m. If the current is 5 A, what is the magnitude of the force acting on the wire?

A. 1.25 N

Correct B. 1.5 N

C. 1.75 N

D. 2 N

Correct Answer: B

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Question 10

A light source is placed at a dis\tance of 1 m from a convex lens of focal length 0.5 m. If the lens is illuminated with a light ray, what is the angle of deviation?

A. 30°

B. 40°

Correct C. 50°

D. 60°

Correct Answer: C

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Question 11

A particle of mass m is moving in a circular orbit of radius r under the influence of a central force F. If the angular momentum of the particle is L, what is the torque acting on the particle?

A. \frac{dL}{dt}

B. \frac{L}{r}

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

Correct D. \frac{FL}{mr}

Correct Answer: D

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Question 12

A block of mass m is attached to a horizontal spring of spring cons\tant k. If 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{k/m}

B. \sqrt{m/k}

C. \sqrt{k/m^2}

D. \sqrt{m/k^2}

Correct Answer: A

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Question 13

A parallel plate capacitor has a capaci\tance of C and is charged to a potential difference of V. If the dis\tance between the plates is increased by a factor of 2, what is the new capaci\tance?

A. C/2

B. C

Correct C. 2C

D. 4C

Correct Answer: C

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Question 14

A coil of wire has a resis\tance of R and an induc\tance of L. If a current of I flows through the coil, what is the induced emf?

A. RI

Correct B. LI

C. R^2I

D. L^2I

Correct Answer: B

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Question 15

A magnetic field of strength B is directed perp\endicular to a current-carrying wire of length L. If the current in the wire is I, what is the force on the wire?

Correct A. BI

B. BL

C. BI^2

D. BL^2

Correct Answer: A

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Question 16

A 2 kg block of ice at 0°C is placed in a 10°C water bath. Assuming the specific heat capacity of ice is 2.05 kJ/kg·K and the specific heat capacity of water is 4.184 kJ/kg·K, calculate the time it takes for the ice to melt completely.

A. 10 minutes

B. 20 minutes

Correct C. 30 minutes

D. 40 minutes

Correct Answer: C

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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 force of 10 N, calculate the time it takes for the particle to complete one revolution.

A. 2 seconds

Correct B. 4 seconds

C. 6 seconds

D. 8 seconds

Correct Answer: B

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Question 18

A convex lens of focal length 20 cm is placed in a beam of light. If the object dis\tance is 30 cm, calculate the image dis\tance.

A. 10 cm

Correct B. 20 cm

C. 30 cm

D. 40 cm

Correct Answer: B

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Question 19

A 10 kg block is attached to a horizontal spring with a force cons\tant of 100 N/m. If the block is displaced by 2 m from its equilibrium position and released, 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 20

A 5 kg block is moving in a straight line with a cons\tant acceleration of 2 m/s^2. If the initial velocity is 4 m/s, calculate the time it takes for the block to reach a velocity of 8 m/s.

A. 2 seconds

Correct B. 4 seconds

C. 6 seconds

D. 8 seconds

Correct Answer: B

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Question 21

A particle of mass $m$ is confined to a one-dimensional box of length $L$. If the energy of the particle is $E$, what is the value of the wave number $k$?

A. \frac{\pi}{L}

B. \frac{2\pi}{L}

Correct C. \frac{\sqrt{2mE}}{\hbar}

D. \frac{2\sqrt{2mE}}{\hbar}

Correct Answer: C

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Question 22

A block of mass $M$ is placed on a horizontal, frictionless surface. A force $F$ is applied to the block, cau\sing it to accelerate at a rate $a$. What is the magnitude of the force $F$?

A. \frac{Ma}{2}

B. \frac{Ma}{4}

Correct C. Ma

D. 2Ma

Correct Answer: C

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Question 23

A simple harmonic oscillator has a frequency of $\omega_0$ and an amplitude of $A$. If the oscillator is displaced from its equilibrium position by a dis\tance $x$, what is the magnitude of the force acting on the oscillator?

Correct A. -m\omega_0^2x

B. m\omega_0^2x

C. 2m\omega_0^2x

D. 3m\omega_0^2x

Correct Answer: A

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Question 24

A radioactive sample decays at a rate given by the equation $\frac{dN}{dt} = -\lambda N$, where $N$ is the number of nuclei and $\lambda$ is the decay cons\tant. If the initial number of nuclei is $N_0$ and the time elapsed is $t$, what is the number of nuclei remaining?

Correct A. N_0 e^{-\lambda t}

B. N_0 e^{\lambda t}

C. N_0 + \lambda t

D. N_0 - \lambda t

Correct Answer: A

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Question 25

A ray of light passes from air into a glass of re\fractive index $n$. If the angle of incidence is $\theta_i$ and the angle of re\fraction is $\theta_r$, what is the value of the angle of re\fraction?

A. \sin \theta_i

B. \cos \theta_i

C. \tan \theta_i

Correct D. \frac{n_1}{n_2} \sin \theta_i

Correct Answer: D

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