POST UTME PAN-ATLANTIC UNIVERSITY 2022 Physics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A quantum particle is confined to a one-dimensional box of length 1 m. If the particle has an energy of 10 eV, what is the wavelength of the particle?
A. 0.1 nm
B. 0.2 nm
C. 0.3 nm
D. 0.4 nm
Question 2
A magnetic field of 0.5 T is applied to a coil of wire with 100 turns and a radius of 0.2 m. If the coil is rotating at a frequency of 50 Hz, what is the induced emf?
A. 10 V
B. 20 V
C. 30 V
D. 40 V
Question 3
A block of mass 5 kg is attached to a horizontal spring with a force cons\tant of 200 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
C. 6 m/s
D. 8 m/s
Question 4
A radioactive sample emits \alpha particles with a half-life of 5 days. If the initial activity is 100 Bq, calculate the activity after 10 days.
A. 12.5 Bq
B. 25 Bq
C. 50 Bq
D. 100 Bq
Question 5
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 subject to a centripetal force of 12 N, what is the magnitude of the force due to friction?
A. 8 N
B. 12 N
C. 16 N
D. 24 N
Question 6
A parallel plate capacitor has plates of area $A$ and separation $d$. The capacitor is connected to a battery of emf $V$. What is the capaci\tance of the capacitor?
A. \frac{\epsilon_0 A}{d}
B. \frac{\epsilon_0 A}{2d}
C. \frac{2\epsilon_0 A}{d}
D. \frac{\epsilon_0 A}{3d}
Question 7
A projectile is launched from the ground with an initial velocity of 20 m/s at an angle of 30° above the horizontal. What is the maximum height reached by the projectile?
A. 10 m
B. 15 m
C. 20 m
D. 25 m
Question 8
A gas at $300\,\text{K}$ is compressed from $0.1\,\text{m}^3$ to $0.05\,\text{m}^3$. If the initial pressure is $10^5\,\text{Pa}$, what is the final pressure?
A. 5\times10^4\,\text{Pa}
B. 10^5\,\text{Pa}
C. 2\times10^5\,\text{Pa}
D. 5\times10^5\,\text{Pa}
Question 9
A circuit consists of a 12 V battery, a 4 Ω resistor, and an inductor of induc\tance 2 H. The circuit is connected to a switch that is initially open. At time $t=0$, the switch is closed. What is the current in the circuit at time $t=0$?
A. 0 A
B. 2 A
C. 4 A
D. 6 A
Question 10
A convex lens of focal length 20 cm forms an image of an object placed 30 cm away. Calculate the magnification of the image.
A. 0.5
B. 1
C. 2
D. 3
Question 11
A parallel-plate capacitor consists of two plates of area A, separated by a dis\tance d. The capaci\tance of the capacitor is given by C = εA/d. Calculate the energy stored in the capacitor when it is charged to a potential difference V.
A. 1/2 CV^2
B. CV^2
C. V^2/C
D. 1/CV^2
Question 12
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\( \frac{npi x}{L}\right \)$, where $n$ is a positive integer. What is the expectation value of the position of the particle?
A. L/2
B. L/nπ
C. L/\( n+1 \)π
D. L/\( n-1 \)π
Question 13
A measurement of 5.0 m is made with an uncertainty of 0.1 m. What is the relative uncertainty?
A. 0.02
B. 0.03
C. 0.04
D. 0.05
Question 14
A 10 μF capacitor is connected in series with a 50 Ω resistor. The circuit is connected to a 12 V battery. What is the time cons\tant of the circuit?
A. 0.5 s
B. 1 s
C. 2 s
D. 5 s
Question 15
A radioactive sample has a half-life of $10\,\text{years}$. If the initial activity is $100\,\text{Bq}$, what is the activity after $20\,\text{years}$?
A. 25\,\text{Bq}
B. 50\,\text{Bq}
C. 75\,\text{Bq}
D. 100\,\text{Bq}

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