POST UTME UNILORIN 2022 Physics | Objective

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Question 1
A circuit consists of a resistor $R$, an inductor $L$, and a capacitor $C$ connected in series. If the circuit is driven by a \sinusoidal voltage source of frequency $f$ and amplitude $V_0$, find the impedance $Z$ of the circuit.
A. Z = \sqrt{R^2 + \( X_L + X_C \)^2}
B. Z = \sqrt{R^2 + \( X_L - X_C \)^2}
C. Z = \sqrt{R^2 + \( X_L + X_C \)^2}
D. Z = \sqrt{R^2 + \( X_L - X_C \)^2}
Question 2
A gas is enclosed in a container with a movable piston. The gas is heated at cons\tant pressure. Which of the following statements is true about the change in volume of the gas?
A. The volume of the gas increases exponentially.
B. The volume of the gas increases linearly with temperature.
C. The volume of the gas remains cons\tant.
D. The volume of the gas decreases exponentially.
Question 3
A sound wave of frequency $f$ and amplitude $A$ is traveling through a medium of density $\rho$ and speed of sound $v_s$. If the wave is reflected from a rigid surface, what is the amplitude of the reflected wave?
A. A_r = A \left\( \frac{v_s - v_i}{v_s + v_i} \right \)^2
B. A_r = A \left\( \frac{v_s + v_i}{v_s - v_i} \right \)^2
C. A_r = A \left\( \frac{v_s - v_i}{v_s + v_i} \right \)
D. A_r = A \left\( \frac{v_s + v_i}{v_s - v_i} \right \)
Question 4
A particle of mass $m$ is moving in a circular orbit of radius $r$ in a potential $V(r) = \frac{k}{r}$. If the particle's angular momentum is $L = 2 mu r^2 omega$, where $mu$ is the reduced mass and $omega$ is the angular frequency, find the total energy $E$ of the particle.
A. E = \frac{1}{2} m r^2 \omega^2 + \frac{k}{r}
B. E = \frac{1}{2} m r^2 \omega^2 - \frac{k}{r}
C. E = \frac{1}{2} m r^2 \omega^2 + \frac{k}{r^2}
D. E = \frac{1}{2} m r^2 \omega^2 - \frac{k}{r^2}
Question 5
A 0.500 kg block is moving in a straight line with a speed of 2.00 m/s. If the block is brought to rest in 0.200 s, what is the average force applied to the block?
A. 1.00 N
B. 2.00 N
C. 3.00 N
D. 4.00 N
Question 6
A 0.500 kg object is attached to a horizontal, massless string and rotated in a circle with a radius of 0.200 m. If the object is rotating at a frequency of 2.00 Hz, what is the tension in the string?
A. 1.00 N
B. 2.00 N
C. 3.00 N
D. 4.00 N
Question 7
A circuit consists of a resistor $R$, an inductor $L$, and a capacitor $C$ connected in series. If the circuit is driven by a voltage source of amplitude $V_0$ and frequency $f$, what is the impedance of the circuit?
A. Z = \sqrt{R^2 + \( X_L - X_C \)^2}
B. Z = \sqrt{R^2 + \( X_L + X_C \)^2}
C. Z = \sqrt{R^2 - \( X_L - X_C \)^2}
D. Z = \sqrt{R^2 - \( X_L + X_C \)^2}
Question 8
A circuit consists of a resistor $R$, an inductor $L$, and a capacitor $C$ connected in series. If the circuit is driven by an alternating voltage source of frequency $f$, find the impedance $Z$ of the circuit.
A. Z = \sqrt{R^2 + \( X_L - X_C \)^2}
B. Z = \sqrt{R^2 + \( X_L + X_C \)^2}
C. Z = \sqrt{R^2 - \( X_L - X_C \)^2}
D. Z = \sqrt{R^2 - \( X_L + X_C \)^2}
Question 9
A block of mass 5 kg is attached to a horizontal, massless spring with a force cons\tant of 200 N/m. The block is displaced by 0.2 m from its equilibrium position and released from rest. Assuming the motion is simple harmonic, calculate the maximum speed of the block as it passes through the equilibrium position.
A. 2 m/s
B. 4 m/s
C. 6 m/s
D. 8 m/s
Question 10
A light ray passes from air into a glass of re\fractive index 1.5. If the angle of incidence is 30°, what is the angle of re\fraction?
A. 20°
B. 30°
C. 40°
D. 50°
Question 11
A light wave of wavelength $\lambda$ and frequency $f$ is incident on a double-slit apparatus. If the dis\tance between the slits is $d$ and the screen is at a dis\tance $D$ from the slits, find the location of the $n^{th}$ bright fringe on the screen.
A. y_n = \frac{n \lambda D}{d}
B. y_n = \frac{\( 2n-1 \) \lambda D}{2d}
C. y_n = \frac{n \lambda D}{2d}
D. y_n = \frac{\( 2n-1 \) \lambda D}{d}
Question 12
A 2.00 kg block is attached to a horizontal, massless spring with a force cons\tant of 100 N/m. The block is displaced by 0.200 m from its equilibrium position and released from rest. What is the speed of the block when it passes through the equilibrium position?
A. 0.400 m/s
B. 0.800 m/s
C. 1.00 m/s
D. 1.20 m/s
Question 13
A 2 kg object is moving in a circular path with a cons\tant speed of 4 m/s. If the radius of the path is 3 m, calculate the centripetal force acting on the object.
A. 10 N
B. 20 N
C. 30 N
D. 40 N
Question 14
A parallel plate capacitor consists of two plates, each of area 0.1 m^2, separated by a dis\tance of 0.01 m. If the plates are charged to a potential difference of 10 V, what is the energy stored in the capacitor?
A. 0.5 J
B. 1 J
C. 5 J
D. 10 J
Question 15
A sample of radioactive material has a half-life of $T_{1/2}$. If the initial activity is $A_0$, find the activity $A$ after a time $t$.
A. A = A_0 \left\( \frac{1}{2}\right \)^{t/T_{1/2}}
B. A = A_0 \left\( \frac{1}{2}\right \)^{T_{1/2}/t}
C. A = A_0 \left\( \frac{1}{2}\right \)^{t/2T_{1/2}}
D. A = A_0 \left\( \frac{1}{2}\right \)^{2T_{1/2}/t}

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