Exam Body

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Subject

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POST UTME AAUA 2017 Physics | Objective

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Question 1

A particle of mass $m$ is confined to a one-dimensional box of length $L$. The wave function of the particle is given by (psi(x) = \sqrt{\frac{2}{L}} \sinleft$ \frac{npi x}{L}\right $). What is the expectation value of the position of the particle?

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 magnetic field of magnitude $B$ is directed perp\endicular to a current-carrying wire of length $L$. The wire carries a current of $I$ and has a resis\tance of $R$. What is the force experienced by the wire?

A. BIL

Correct B. BIL\sin\theta

C. BIL\cos\theta

D. BIL\tan\theta

Correct Answer: B

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Question 3

A gas of $N$ molecules is confined to a container of volume $V$. The molecules are assumed to be non-interacting and have a mass of $m$. What is the average kinetic energy of the molecules?

Correct A. \frac{3}{2} \frac{p^2}{m}

B. \frac{3}{2} \frac{p^2}{mV}

C. \frac{3}{2} \frac{p^2}{m^2}

D. \frac{3}{2} \frac{p^2}{m^3}

Correct Answer: A

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Question 4

A projectile is launched from the origin with an initial velocity of $v_0$ at an angle of $\theta$ above the horizontal. What is the maximum height reached by the projectile?

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

B. \frac{v_0^2 \cos^2\theta}{2g}

C. \frac{v_0^2 \sin\theta}{2g}

D. \frac{v_0^2 \cos\theta}{2g}

Correct Answer: A

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Question 5

A nucleus of mass $A$ undergoes radioactive decay, emitting an \alpha particle of mass $m$. What is the energy released in the decay?

Correct A. $ m_A - 2m $ c^2

B. $ m_A - m $ c^2

C. $ m_A + m $ c^2

D. $ m_A - 4m $ c^2

Correct Answer: A

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Question 6

A ray of light passes from air into a glass slab at an angle of incidence of 30°. If the re\fractive index of the glass is 1.5, calculate the angle of re\fraction.

A. 20°

Correct B. 25°

C. 30°

D. 35°

Correct Answer: B

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Question 7

A block of mass 5 kg is attached to a horizontal spring with a spring cons\tant of 200 N/m. If the block is displaced by 0.2 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 8

A car travels from point A to point B with an average speed of 60 km/h. If the dis\tance between points A and B is 240 km, calculate the time taken by the car to travel from point A to point B.

A. 2 hours

Correct B. 3 hours

C. 4 hours

D. 5 hours

Correct Answer: B

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Question 9

A body of mass 10 kg is moving with a velocity of 20 m/s. If the body is subjected to a force of 50 N, calculate the acceleration of the body.

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 10

A ray of light passes from a glass slab into air at an angle of incidence of 40°. If the re\fractive index of the glass is 1.2, calculate the angle of re\fraction.

A. 25°

Correct B. 30°

C. 35°

D. 40°

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 experiences a centripetal acceleration of 2 m/s^2, what is the magnitude of the force acting on the particle?

A. 10 N

B. 12 N

Correct C. 16 N

D. 20 N

Correct Answer: C

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Question 12

A parallel plate capacitor has a capaci\tance of 5 μF and is charged to a potential difference of 10 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. 6.25 μF

B. 7.5 μF

Correct C. 8.33 μF

D. 10 μF

Correct Answer: C

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Question 13

A projectile is launched from the ground with an initial velocity of 20 m/s at an angle of 30° above the horizontal. If air resis\tance is neglected, what is the maximum height reached by the projectile?

A. 10 m

B. 12 m

Correct C. 15 m

D. 18 m

Correct Answer: C

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Question 14

A circuit consists of a 10 Ω resistor, a 20 Ω resistor, and a 5 Ω resistor connected in series. If a voltage of 15 V is applied across the circuit, what is the current flowing through the 5 Ω resistor?

A. 0.5 A

B. 1 A

Correct C. 1.5 A

D. 2 A

Correct Answer: C

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Question 15

A wave function is given by ψ(x) = Ae^(ikx). If the wave function is normalized, what is the value of A?

Correct A. 1/√2

B. 1/√π

C. 1/√2π

D. 1/√π^2

Correct Answer: A

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Question 16

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 17

A photon of energy 6 eV is incident on a metal surface with a work function of 4 eV. What is the maximum kinetic energy of the electron emitted?

A. 2 eV

Correct B. 4 eV

C. 6 eV

D. 8 eV

Correct Answer: B

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Question 18

A radioactive sample has a half-life of 5 years. If the initial activity is 100 Bq, what is the activity after 10 years?

Correct A. 12.5 Bq

B. 25 Bq

C. 50 Bq

D. 100 Bq

Correct Answer: A

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Question 19

A charged particle of mass 1 kg and charge 2 C is moving in a magnetic field of strength 0.5 T. If the particle has a velocity of 3 m/s, what is the magnitude of the force acting on the particle?

A. 0.5 N

B. 1 N

Correct C. 2 N

D. 3 N

Correct Answer: C

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Question 20

A capacitor of capaci\tance 10 μF is connected to a battery of voltage 12 V. If the capacitor is initially uncharged, what is the charge on the capacitor after 5 minutes?

A. 120 μC

B. 240 μC

C. 360 μC

Correct D. 480 μC

Correct Answer: D

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Question 21

A parallel plate capacitor has a capaci\tance of 10 μF. If a potential difference of 100 V is applied across it, what is the charge stored on the plates?

Correct A. 0.1 C

B. 10 C

C. 100 C

D. 1000 C

Correct Answer: A

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Question 22

A 100 Ω resistor is connected in series with a 200 Ω resistor and a 300 Ω resistor. What is the total resis\tance of the circuit?

A. 400 Ω

B. 500 Ω

Correct C. 600 Ω

D. 700 Ω

Correct Answer: C

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Question 23

A particle moves in a circular path with a cons\tant speed of 5 m/s. If the radius of the circle is 2 m, what is the magnitude of the centripetal acceleration?

A. 2 m/s^2

B. 5 m/s^2

Correct C. 10 m/s^2

D. 20 m/s^2

Correct Answer: C

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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 0.2 m from its equilibrium position and released, what is the maximum speed of the block?

A. 0.5 m/s

B. 1 m/s

Correct C. 2 m/s

D. 5 m/s

Correct Answer: C

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Question 25

A \tank contains 1000 kg of water at a depth of 10 m. What is the pressure at the bottom of the \tank?

A. 100 kPa

B. 200 kPa

Correct C. 500 kPa

D. 1000 kPa

Correct Answer: C

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