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POST UTME ABU 2024 Physics | Objective

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Question 1

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 net 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 2

A 100 V AC supply is connected across a 50 Ω resistor. If the current through the resistor is 2 A, what is the power consumed by the resistor?

A. 50 W

Correct B. 100 W

C. 200 W

D. 250 W

Correct Answer: B

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Question 3

A uniform rod of length 2 m and mass 5 kg is placed on a smooth horizontal surface. If a force of 10 N is applied at one \end of the rod, what is the acceleration of the rod?

A. 0.5 m/s^2

B. 1 m/s^2

Correct C. 2 m/s^2

D. 5 m/s^2

Correct Answer: C

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Question 4

A 10 kg object is susp\ended from a spring with a spring cons\tant of 100 N/m. If the object is displaced by 2 m from its equilibrium position, what is the potential energy stored in the spring?

A. 20 J

B. 40 J

Correct C. 60 J

D. 80 J

Correct Answer: C

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Question 5

A 5 kg object is moving in a circular path of radius 4 m with a cons\tant speed of 3 m/s. If the object is subjected to a centripetal acceleration of 1 m/s^2, what is the magnitude of the net force acting on the object?

A. 10 N

B. 15 N

Correct C. 20 N

D. 25 N

Correct Answer: C

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Question 6

A particle of mass 2 kg is attached to a spring with spring cons\tant 100 N/m. It is displaced by 0.2 m from its equilibrium position and released from rest. Assuming the motion is simple harmonic, calculate the total energy of the particle at time t = 0.

A. 10 J

Correct B. 20 J

C. 30 J

D. 40 J

Correct Answer: B

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Question 7

A block of mass 5 kg is placed on a frictionless surface and attached to a horizontal spring with spring cons\tant 200 N/m. The block is displaced by 0.1 m from its equilibrium position and released from rest. Assuming the motion is simple harmonic, calculate the angular frequency of the block.

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 8

A particle of mass 3 kg is moving in a circular path with a radius of 0.5 m. The particle is moving at a speed of 4 m/s. Calculate the centripetal 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 9

A car of mass 1500 kg is traveling at a speed of 25 m/s. The driver applies the brakes, and the car comes to a stop in 4 s. Assuming the force of friction is cons\tant, calculate the average force of friction acting on the car.

Correct A. 3750 N

B. 375 N

C. 3.75 N

D. 37500 N

Correct Answer: A

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Question 10

A block of mass 2 kg is placed on a frictionless surface and attached to a horizontal spring with spring cons\tant 100 N/m. The block is displaced by 0.2 m from its equilibrium position and released from rest. Assuming the motion is simple harmonic, calculate the kinetic energy of the block at time t = 0.

A. 10 J

Correct B. 20 J

C. 30 J

D. 40 J

Correct Answer: B

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Question 11

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 force?

A. 10 N

Correct B. 12 N

C. 15 N

D. 20 N

Correct Answer: B

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Question 12

A wave has a frequency of 200 Hz and a wavelength of 0.5 m. If the wave is traveling at a speed of 100 m/s, what is the amplitude of the wave?

Correct A. 0.25 m

B. 0.5 m

C. 0.75 m

D. 1 m

Correct Answer: A

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Question 13

A gas is heated from 20°C to 80°C. If the initial volume of the gas is 2 L and the final volume is 4 L, what is the change in temperature?

A. 10°C

Correct B. 20°C

C. 30°C

D. 40°C

Correct Answer: B

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Question 14

A particle is moving in a one-dimensional potential well. If the particle has a wave function given by \psi(x) = Ae^{-\alpha x^2}, what is the probability of finding the particle between x = 0 and x = 1?

A. 0.5

Correct B. 0.6

C. 0.7

D. 0.8

Correct Answer: B

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Question 15

A block of mass 5 kg is 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 16

A solid sphere of radius R is made of a material with a Young's modulus of 200 GPa. If the sphere is subjected to a hydrostatic pressure of 100 MPa, what is the resulting change in its volume?

A. 0.05%

Correct B. 0.1%

C. 0.2%

D. 0.5%

Correct Answer: B

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Question 17

A convex lens of focal length 20 cm is placed in contact with a concave lens of focal length -15 cm. What is the focal length of the combination?

Correct A. 10 cm

B. 15 cm

C. 20 cm

D. 25 cm

Correct Answer: A

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Question 18

A sound wave with a frequency of 200 Hz and a speed of 340 m/s is traveling through a medium. If the wavelength of the wave is 1.7 m, what is the amplitude of the wave?

A. 0.05 m

Correct B. 0.1 m

C. 0.2 m

D. 0.5 m

Correct Answer: B

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Question 19

A capacitor consists of two parallel plates, each with a surface area of 0.1 m^2. The dis\tance between the plates is 0.01 m. If a potential difference of 10 V is applied across the capacitor, what is the capaci\tance?

A. 10^-6 F

Correct B. 10^-5 F

C. 10^-4 F

D. 10^-3 F

Correct Answer: B

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Question 20

A resistor of 10 ohms is connected in series with a capacitor of 100 microfarads and an inductor of 50 millihenrys. If an alternating current of 5 amps is applied across the circuit, what is the impedance of the circuit?

A. 10 ohms

B. 20 ohms

Correct C. 30 ohms

D. 40 ohms

Correct Answer: C

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Question 21

A particle of mass $m$ is confined to a one-dimensional box of length $L$. If the particle is in the ground state, what is the expectation value of its position?

A. 0

Correct B. L/2

C. L

D. 2L

Correct Answer: B

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Question 22

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 the maximum speed of the block?

Correct A. \sqrt{\frac{k}{m}}x

B. \sqrt{\frac{k}{m}}x^2

C. \frac{k}{m}x

D. \frac{k}{m}x^2

Correct Answer: A

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Question 23

A parallel plate capacitor has plates of area $A$ and separation $d$. If the capacitor is charged to a potential difference $V$, what is the electric field between the plates?

A. \frac{V}{A}

Correct B. \frac{V}{d}

C. \frac{V}{A^2}

D. \frac{V}{d^2}

Correct Answer: B

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Question 24

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

Correct A. \sin^{-1} \frac{n_1}{n_2} \sin \theta_i

B. \sin^{-1} \frac{n_2}{n_1} \sin \theta_i

C. \sin^{-1} \frac{n_1}{n_2} \cos \theta_i

D. \sin^{-1} \frac{n_2}{n_1} \cos \theta_i

Correct Answer: A

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Question 25

A lens of focal length $f$ forms an image of an object at a dis\tance $x$ from the lens. If the object is moved to a dis\tance $2x$, what is the new image dis\tance?

A. \frac{2x}{3}

Correct B. \frac{3x}{2}

C. \frac{x}{2}

D. \frac{2x}{5}

Correct Answer: B

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