Practice post utme eksu physics 2017 Past Questions

Question 1

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?

Correct A. \frac{L}{2}

B. \frac{L}{4}

C. \frac{3L}{4}

D. \frac{L}{3}

Correct Answer: A

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Question 2

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

Correct A. \sqrt{R^2 + $ \omega L - \frac{1}{\omega C} $^2}

B. \frac{1}{\sqrt{R^2 + $ \omega L - \frac{1}{\omega C} $^2}}

C. \omega L - \frac{1}{\omega C}

D. R + \omega L - \frac{1}{\omega C}

Correct Answer: A

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Question 3

A projectile is launched from the origin with an initial velocity $v_0$ at an angle $\theta$ above the horizontal. If the projectile lands at a dis\tance $d$ from the origin, what is the time of flight?

Correct A. \frac{2v_0 \sin \theta}{g}

B. \frac{v_0 \sin \theta}{g}

C. \frac{2v_0 \cos \theta}{g}

D. \frac{v_0 \cos \theta}{g}

Correct Answer: A

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Question 4

A wire of length $L$ and resis\tance $R$ is stretched to a length $2L$ while its cross-sectional area is reduced to $\frac{1}{4}$ of its original value. What is the new resis\tance?

Correct A. 16R

B. 4R

C. 2R

D. R

Correct Answer: A

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Question 5

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

Correct A. ILB

B. \frac{ILB}{L}

C. \frac{ILB}{B}

D. \frac{ILB}{I}

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 force of 12 N, what is the magnitude of the acceleration of the particle?

A. 6 m/s^2

Correct B. 12 m/s^2

C. 18 m/s^2

D. 24 m/s^2

Correct Answer: B

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Question 7

A 10 μF capacitor is connected in series with a 20 Ω resistor and a 100 V battery. What is the time cons\tant of the circuit?

Correct A. 2 ms

B. 4 ms

C. 6 ms

D. 8 ms

Correct Answer: A

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Question 8

A 5 kg block is attached to a horizontal, massless spring with a force cons\tant of 100 N/m. The block is displaced by 2 m from its equilibrium position and released from rest. What is the maximum speed of the block?

A. 4 m/s

B. 6 m/s

Correct C. 8 m/s

D. 10 m/s

Correct Answer: C

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Question 9

A 2000 μF capacitor is connected in parallel with a 1000 μF capacitor. What is the equivalent capaci\tance of the circuit?

A. 1000 μF

B. 2000 μF

Correct C. 3000 μF

D. 4000 μF

Correct Answer: C

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Question 10

A 50 Ω resistor is connected in series with a 20 Ω resistor and a 100 V battery. What is the current in the circuit?

A. 1 A

Correct B. 1.5 A

C. 2 A

D. 2.5 A

Correct Answer: B

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Question 11

A gas is enclosed in a container of volume 2.5 L at a temperature of 300 K. If the temperature is increased to 500 K, what is the new volume of the gas, assuming ideal gas behavior?

A. 3.125 L

Correct B. 4.166 L

C. 5.208 L

D. 6.25 L

Correct Answer: B

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Question 12

A sound wave with a frequency of 200 Hz has a wavelength of 1.5 m. What is the speed of the sound wave?

A. 300 m/s

B. 360 m/s

Correct C. 420 m/s

D. 480 m/s

Correct Answer: C

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Question 13

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

A. 8 Ω

B. 10 Ω

C. 12 Ω

Correct D. 14 Ω

Correct Answer: D

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Question 14

A particle is moving in a circular path with a radius of 2 m. If the particle completes one revolution in 4 s, what is its angular velocity?

A. 0.5 rad/s

B. 1 rad/s

C. 2 rad/s

Correct D. 4 rad/s

Correct Answer: D

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Question 15

A force of 10 N is applied to an object, cau\sing it to accelerate at 2 m/s^2. What is the mass of the object?

A. 2.5 kg

B. 5 kg

Correct C. 10 kg

D. 20 kg

Correct Answer: C

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Question 16

A 50 Hz AC voltage source is connected to a 100 Ω resistor in series with a 20 μF capacitor. If the initial phase angle between the voltage and current is 30°, calculate the impedance of the circuit.

A. 120 Ω

B. 140 Ω

Correct C. 160 Ω

D. 180 Ω

Correct Answer: C

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Question 17

A sound wave with a frequency of 200 Hz has a wavelength of 1.5 m. Calculate the speed of the sound wave.

A. 300 m/s

Correct B. 400 m/s

C. 500 m/s

D. 600 m/s

Correct Answer: B

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Question 18

A quantum particle has a wave function given by $ \psi(x) = Ae^{-\alpha x^2} $. If the average value of the position is 0.5 m, calculate the s\tandard deviation of the position.

A. 0.1 m

B. 0.2 m

Correct C. 0.3 m

D. 0.4 m

Correct Answer: C

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Question 19

A convex lens has a focal length of 20 cm. If an object is placed 30 cm in front of the lens, 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 20

A vector $ \vec{A} $ has a magnitude of 5 units and makes an angle of 60° with the x-axis. If a second vector $ \vec{B} $ has a magnitude of 3 units and makes an angle of 30° with the x-axis, calculate the magnitude of the resul\tant vector $ \vec{A} + \vec{B} $.

A. 6 units

B. 7 units

Correct C. 8 units

D. 9 units

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. 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 22

A parallel plate capacitor has a capaci\tance of 10 μF and is charged to a potential difference of 20 V. If a dielectric slab of thickness 2 mm and dielectric cons\tant 3 is inserted between the plates, what is the new capaci\tance?

A. 30 μF

B. 40 μF

Correct C. 50 μF

D. 60 μF

Correct Answer: C

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Question 23

A radioactive sample has an initial activity of 100 Bq. If the half-life of the sample is 2 hours, what is the activity after 4 hours?

A. 25 Bq

Correct B. 50 Bq

C. 75 Bq

D. 100 Bq

Correct Answer: B

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Question 24

A block of mass 5 kg 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, 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 25

A current of 2 A flows through a resistor of 10 Ω. If the voltage across the resistor is 20 V, what is the power dissipated by the resistor?

A. 40 W

Correct B. 60 W

C. 80 W

D. 100 W

Correct Answer: B

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