POST UTME PAN-ATLANTIC UNIVERSITY 2020 Physics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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
C. 6 m/s^2
D. 8 m/s^2
Question 2
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. \( \sqrt{\frac{2k}{m}} \)
C. \( \sqrt{\frac{4k}{m}} \)
D. \( \sqrt{\frac{8k}{m}} \)
Question 3
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
C. 30 N
D. 40 N
Question 4
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 operator for this particle?
A. 0
B. \frac{L}{2}
C. L
D. \frac{nL}{2}
Question 5
A lens has a focal length of $f$. A light ray passes through the lens and is re\fracted. The angle of incidence is $i$, the angle of re\fraction is $r$, and the angle of deviation is $D$. What is the relationship between these angles?
A. D = i + r
B. D = i - r
C. D = \frac{i}{f}
D. D = \frac{i}{2f}
Question 6
A circuit consists of a resistor $R$, an inductor $L$, and a capacitor $C$ connected in series. The impedance of the circuit is given by $Z = \sqrt{R^2 + \( \omega L - \frac{1}{\omega C} \)^2}$. What is the condition for resonance to occur?
A. \omega L - \frac{1}{\omega C} = 0
B. \omega L + \frac{1}{\omega C} = 0
C. \omega L - \frac{1}{\omega C} = \frac{1}{2}
D. \omega L + \frac{1}{\omega C} = \frac{1}{2}
Question 7
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
B. 2 A
C. 3 A
D. 4 A
Question 8
A parallel plate capacitor has plates of area 0.04 m^2 and separation 0.02 m. If the dielectric cons\tant of the material between the plates is 3, calculate the capaci\tance.
A. 0.04 F
B. 0.08 F
C. 0.12 F
D. 0.16 F
Question 9
A simple harmonic motion is described by the equation $x(t) = A \cos\( omega t + phi \)$, where $A$ is the amplitude, $omega$ is the angular frequency, and $phi$ is the phase angle. What is the velocity of the particle at time $t = 0$?
A. -A\omega \sin\( \phi \)
B. A\omega \sin\( \phi \)
C. -A\omega \cos\( \phi \)
D. A\omega \cos\( \phi \)
Question 10
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?
A. \frac{v^2}{r}
B. \frac{2v^2}{r}
C. \frac{3v^2}{r}
D. \frac{4v^2}{r}
Question 11
A light ray passes through a prism and is re\fracted. The angle of incidence is $i$, the angle of re\fraction is $r$, and the angle of deviation is $D$. What is the relationship between these angles?
A. D = i + r
B. D = i - r
C. D = i + 2r
D. D = i - 2r
Question 12
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
C. 30 minutes
D. 40 minutes
Question 13
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
C. 6 m/s^2
D. 8 m/s^2
Question 14
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?
A. \frac{L}{2}
B. \frac{L}{4}
C. \frac{3L}{4}
D. \frac{L}{3}
Question 15
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
C. 3 s
D. 4 s

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