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POST UTME PAN-ATLANTIC UNIVERSITY 2020 Physics | Objective

Are you preparing for POST UTME PAN-ATLANTIC UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2020 Physics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

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

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 radioactive sample decays with a half-life of $T_{1/2} = 10$ years. If the initial activity is $A_0 = 100$ Bq, what is the activity of the sample after $t = 20$ years?

A. 50 Bq

B. 25 Bq

Correct C. 12.5 Bq

D. 6.25 Bq

Correct Answer: C

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Question 3

A circuit consists of a 12 V battery, a 4 Ω resistor, and a 6 Ω resistor connected in series. What is the current flowing through the circuit?

A. 1.5 A

Correct B. 2 A

C. 3 A

D. 4 A

Correct Answer: B

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Question 4

A force of magnitude $F = 10$ N acts on an object of mass $m = 2$ kg. If the object is moving in a circular path with a radius of $r = 3$ m, what is the magnitude of the centripetal acceleration?

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 5

A particle of mass $m$ is moving in a circular path with a radius of $r$. If the particle is subject to a centripetal force of magnitude $F_c = \frac{mv^2}{r}$, what is the magnitude of the acceleration of the particle?

Correct A. \frac{v^2}{r}

B. \frac{2v^2}{r}

C. \frac{3v^2}{r}

D. \frac{4v^2}{r}

Correct Answer: A

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Question 6

In a region where the magnetic field is uniform and cons\tant, a coil of wire with 50 turns and a radius of 0.05 m is placed perp\endicular to the magnetic field. If the magnetic field strength is 0.2 T, calculate the induced emf in the coil when it is rotated by 90° in 0.1 s.

A. 0.5 V

Correct B. 1.0 V

C. 1.5 V

D. 2.0 V

Correct Answer: B

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Question 7

A particle of mass 2 kg is moving in a circular path with a radius of 3 m. If the particle's velocity is 4 m/s, calculate the force required to keep the particle in circular motion.

A. 10 N

B. 20 N

Correct C. 30 N

D. 40 N

Correct Answer: C

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Question 8

A wave with a frequency of 50 Hz and a wavelength of 10 m is traveling through a medium. Calculate the speed of the wave.

A. 500 m/s

Correct B. 1000 m/s

C. 1500 m/s

D. 2000 m/s

Correct Answer: B

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Question 9

A circuit consists of a 10 Ω resistor, a 20 Ω resistor, and a 5 Ω resistor connected in parallel. If the voltage across the circuit is 20 V, calculate the current through the 10 Ω resistor.

A. 2 A

Correct B. 4 A

C. 6 A

D. 8 A

Correct Answer: B

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Question 10

A particle of mass 1 kg is moving in a circular path with a radius of 2 m. If the particle's velocity is 3 m/s, calculate the force required to keep the particle in circular motion.

A. 3 N

B. 6 N

Correct C. 9 N

D. 12 N

Correct Answer: C

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Question 11

A particle of mass ( m ) is moving in a circular path of radius ( r ) with a cons\tant speed ( v ). The particle is subject to a centripetal force $ F_c $ given by $ F_c = \frac{mv^2}{r} $. If the particle's speed is doubled, what is the new centripetal force required to keep the particle in its circular path?

A. $ \frac{mv^2}{r} $

B. $ \frac{2mv^2}{r} $

Correct C. $ \frac{4mv^2}{r} $

D. $ \frac{8mv^2}{r} $

Correct Answer: C

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Question 12

A capacitor consists of two parallel plates of area ( A ) separated by a dis\tance ( d ). The plates are charged to a potential difference ( V ). The capaci\tance ( C ) of the capacitor is given by $ C = \frac{epsilon_0 A}{d} $. If the area of the plates is doubled, what is the new capaci\tance?

A. $ \frac{epsilon_0 A}{d} $

B. $ \frac{2epsilon_0 A}{d} $

Correct C. $ \frac{4epsilon_0 A}{d} $

D. $ \frac{8epsilon_0 A}{d} $

Correct Answer: C

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Question 13

A circuit consists of a resistor ( R ) and an inductor ( L ) connected in series. The circuit is driven by a voltage source ( V ) with a frequency ( f ). The impedance ( Z ) of the circuit is given by $ Z = \sqrt{R^2 + \( 2pi f L \ $^2} ). If the frequency is doubled, what is the new impedance?

A. $ \sqrt{R^2 + \( 2pi f L \ $^2} )

B. $ \sqrt{R^2 + \( 4pi f L \ $^2} )

Correct C. $ \sqrt{R^2 + \( 8pi f L \ $^2} )

D. $ \sqrt{R^2 + \( 16pi f L \ $^2} )

Correct Answer: C

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Question 14

A block of mass ( m ) is attached to a horizontal spring with a spring cons\tant ( k ). The block is displaced by a dis\tance ( x ) from its equilibrium position and released from rest. The block's motion is described by the equation ( x(t) = A \cos(omega t) ), where $ omega = \sqrt{\frac{k}{m}} $. If the spring cons\tant is doubled, what is the new angular frequency?

A. $ \sqrt{\frac{k}{m}} $

B. $ \sqrt{\frac{2k}{m}} $

Correct C. $ \sqrt{\frac{4k}{m}} $

D. $ \sqrt{\frac{8k}{m}} $

Correct Answer: C

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Question 15

A parallel-plate capacitor consists of two plates of area ( A ) separated by a dis\tance ( d ). The plates are charged to a potential difference ( V ). The capaci\tance ( C ) of the capacitor is given by $ C = \frac{epsilon_0 A}{d} $. If the dis\tance between the plates is doubled, what is the new capaci\tance?

A. $ \frac{epsilon_0 A}{d} $

Correct B. $ \frac{2epsilon_0 A}{d} $

C. $ \frac{4epsilon_0 A}{d} $

D. $ \frac{8epsilon_0 A}{d} $

Correct Answer: B

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Question 16

A sound wave with a frequency of 200 Hz is produced by a source moving towards a stationary observer. If the speed of sound in air is 343 m/s, what is the apparent frequency heard by the observer?

A. 220 Hz

Correct B. 240 Hz

C. 260 Hz

D. 280 Hz

Correct Answer: B

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Question 17

A beam of light passes from air into a glass slab of re\fractive index 1.5. If the angle of incidence is 30°, what is the angle of re\fraction?

A. 20°

Correct B. 25°

C. 30°

D. 35°

Correct Answer: B

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Question 18

A particle of mass 2 kg is moving in a circular path of radius 3 m with a speed of 4 m/s. What is the magnitude of 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 19

A photon of energy 2 eV is incident on a metal surface with a work function of 1.5 eV. What is the maximum kinetic energy of the photoelectron?

A. 0.5 eV

Correct B. 1 eV

C. 1.5 eV

D. 2 eV

Correct Answer: B

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Question 20

A coil of wire with 100 turns is placed in a magnetic field of strength 0.5 T. If the current in the coil is 2 A, what is the magnitude of the torque acting on the coil?

A. 0.1 Nm

Correct B. 0.2 Nm

C. 0.3 Nm

D. 0.4 Nm

Correct Answer: B

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Question 21

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 2090 J/(kg·K) and the latent heat of fusion of ice is 334 kJ/kg, 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 22

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, calculate 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 23

A gas expands from an initial volume of 2 L to a final volume of 5 L against an external pressure of 1 atm. If the initial temperature is 300 K, calculate the work done by the gas.

A. 100 J

B. 200 J

Correct C. 300 J

D. 400 J

Correct Answer: C

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Question 24

A magnetic field of 0.5 T is applied to a coil of wire with 100 turns. If the coil has a resis\tance of 10 Ω, calculate the induced emf in the coil.

A. 0.5 V

Correct B. 1 V

C. 2 V

D. 3 V

Correct Answer: B

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Question 25

A capacitor with a capaci\tance of 10 μF is connected to a 12 V battery. If the capacitor is initially uncharged, calculate the time it takes for the capacitor to reach a voltage of 9 V.

A. 1 s

B. 2 s

Correct C. 3 s

D. 4 s

Correct Answer: C

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