Practice post utme uniport physics 2017 Past Questions

Question 1

A solid cylinder of radius 0.05 m and height 0.2 m is floating in a liquid of density 900 kg/m³. If the density of the solid cylinder is 5000 kg/m³, what is the percentage of the cylinder's volume that is submerged in the liquid?

Correct A. 10%

B. 20%

C. 30%

D. 40%

Correct Answer: A

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Question 2

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?

Correct A. 20°

B. 30°

C. 40°

D. 50°

Correct Answer: A

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Question 3

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

B. 20 N

Correct C. 30 N

D. 40 N

Correct Answer: C

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Question 4

A 5 m long wire is carrying a current of 2 A. If the magnetic field at a dis\tance of 0.5 m from the wire is 0.1 T, what is the direction of the magnetic field?

Correct A. Into the page

B. Out of the page

C. Along the wire

D. Perp\endicular to the wire

Correct Answer: A

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Question 5

A photon of energy 2 eV is incident on a metal surface. If the work function of the metal is 1 eV, what is the maximum kinetic energy of the emitted electron?

A. 1 eV

B. 2 eV

Correct C. 3 eV

D. 4 eV

Correct Answer: C

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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 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 7

A wave of frequency 100 Hz and wavelength 0.5 m is traveling through a medium. If the wave is reflected from a fixed \end, what is the frequency of the reflected wave?

A. 50 Hz

Correct B. 100 Hz

C. 150 Hz

D. 200 Hz

Correct Answer: B

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Question 8

A capacitor of capaci\tance 10 μF is connected in series with a resistor of resis\tance 20 Ω. If a voltage of 50 V is applied across the circuit, what is the current flowing through the circuit?

A. 0.25 A

Correct B. 0.5 A

C. 1 A

D. 2 A

Correct Answer: B

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Question 9

A particle of mass 1 kg is in a state of wave-particle duality. If the particle is described by a wave function ψ(x) = Ae^$ -αx^2 $, what is the probability of finding the particle in the region x = 0 to x = 1?

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 10

A simple harmonic motion has a frequency of 2 Hz and an amplitude of 3 m. If the motion is described by the equation x(t) = 3 \sin(2πt), what is the angular frequency of the motion?

A. 4π rad/s

Correct B. 6π rad/s

C. 8π rad/s

D. 10π rad/s

Correct Answer: B

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Question 11

A parallel plate capacitor has plates of area 0.04 m^2 and separation 0.02 m. If the dielectric cons\tant of the material between the plates is 3, calculate the capaci\tance.

A. 1.6 x 10^-9 F

Correct B. 3.2 x 10^-9 F

C. 4.8 x 10^-9 F

D. 6.4 x 10^-9 F

Correct Answer: B

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Question 12

A magnetic field is produced by a current-carrying wire. If the current is 2 A and the wire is 0.5 m long, calculate the magnetic field at a dis\tance of 0.1 m from the wire.

Correct A. 1.26 x 10^-6 T

B. 2.52 x 10^-6 T

C. 3.78 x 10^-6 T

D. 5.04 x 10^-6 T

Correct Answer: A

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Question 13

A gas is heated from 300 K to 400 K. If the initial volume is 0.5 m^3 and the final volume is 1.5 m^3, calculate the work done.

A. 1.5 x 10^3 J

B. 3.0 x 10^3 J

Correct C. 4.5 x 10^3 J

D. 6.0 x 10^3 J

Correct Answer: C

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Question 14

A ray of light passes from air into a glass 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 15

A sound wave has a frequency of 200 Hz and a wavelength of 0.5 m. If the speed of sound is 340 m/s, calculate the amplitude.

A. 0.05 m

Correct B. 0.1 m

C. 0.15 m

D. 0.2 m

Correct Answer: B

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Question 16

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 angular momentum of the particle is $L = 2mvr$, find the total energy of the particle.

A. E = -\frac{k}{2r}

Correct B. E = -\frac{k}{r}

C. E = \frac{k}{2r}

D. E = \frac{k}{r}

Correct Answer: B

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Question 17

A sound wave with frequency $f$ is traveling through a medium with speed $v$. If the wavelength of the sound wave is $\lambda$, find the time period $T$ of the sound wave.

A. T = \frac{2\pi}{f}

Correct B. T = \frac{2\pi\lambda}{v}

C. T = \frac{2\pi v}{f}

D. T = \frac{2\pi\lambda}{f}

Correct Answer: B

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Question 18

A circuit consists of a resistor $R$, an inductor $L$, and a capacitor $C$ connected in series. If the impedance of the circuit is $Z = \sqrt{R^2 + $ \omega L - \frac{1}{\omega C} $^2}$, find the phase angle $\phi$ of the circuit.

Correct A. \phi = \arc\tan\left$ \frac{\omega L - \frac{1}{\omega C}}{R}\right $

B. \phi = \arc\tan\left$ \frac{R}{\omega L - \frac{1}{\omega C}}\right $

C. \phi = \arc\tan\left$ \frac{R}{\omega L + \frac{1}{\omega C}}\right $

D. \phi = \arc\tan\left$ \frac{\omega L + \frac{1}{\omega C}}{R}\right $

Correct Answer: A

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Question 19

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 angular momentum of the particle is $L = 2mvr$, find the potential energy $U$ of the particle.

Correct A. U = -\frac{k}{r}

B. U = \frac{k}{r}

C. U = -\frac{k}{2r}

D. U = \frac{k}{2r}

Correct Answer: A

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Question 20

A sound wave with frequency $f$ is traveling through a medium with speed $v$. If the wavelength of the sound wave is $\lambda$, find the speed $v$ of the sound wave.

Correct A. v = f\lambda

B. v = \frac{f}{\lambda}

C. v = f\frac{\lambda}{2}

D. v = \frac{f}{2\lambda}

Correct Answer: A

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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. If the particle is subjected to a centripetal force of 12 N, what is the angular velocity of the particle?

A. 2 rad/s

Correct B. 4 rad/s

C. 6 rad/s

D. 8 rad/s

Correct Answer: B

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Question 22

A block of mass 5 kg is placed on a frictionless surface and attached to a horizontal spring with a force cons\tant of 20 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 23

A car of mass 1500 kg is traveling at a speed of 25 m/s when it encounters a hill with an elevation of 100 m. If the car's kinetic energy is converted entirely to potential energy, what is the car's speed at the top of the hill?

A. 10 m/s

B. 15 m/s

Correct C. 20 m/s

D. 25 m/s

Correct Answer: C

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Question 24

A radioactive sample has a half-life of 5 years. If the initial activity of the sample is 1000 Bq, what is the activity of the sample after 10 years?

A. 500 Bq

Correct B. 750 Bq

C. 1000 Bq

D. 1250 Bq

Correct Answer: B

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Question 25

A wave with a frequency of 50 Hz and a wavelength of 2 m is traveling through a medium with a speed of 100 m/s. What is the amplitude of the wave?

A. 0.1 m

B. 0.2 m

Correct C. 0.3 m

D. 0.4 m

Correct Answer: C

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