POST UTME IMS U 2018 Physics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A projectile is launched from the ground with an initial velocity of 20 m/s at an angle of 60° above the horizontal. If the air resis\tance is negligible, calculate the maximum height reached by the projectile.
A. 10.0 m
B. 15.0 m
C. 20.0 m
D. 25.0 m
Question 2
A gas is contained in a cylinder of volume $V$ with a movable piston. The gas is heated, cau\sing its pressure to increase from $P_1$ to $P_2$. Find the work done $W$ by the gas u\sing the formula $W = \int_{V_1}^{V_2} P dV$.
A. W = P_2 \( V_2 - V_1 \)
B. W = P_1 \( V_2 - V_1 \)
C. W = \frac{1}{2} \( P_2 + P_1 \) \( V_2 - V_1 \)
D. W = \frac{1}{2} \( P_2 - P_1 \) \( V_2 - V_1 \)
Question 3
A 2.5 kg block is attached to a horizontal, massless spring with a force cons\tant of 100 N/m. The block is displaced by 0.2 m from its equilibrium position and released from rest. Assuming the block undergoes simple harmonic motion, calculate the maximum speed of the block as it passes through the equilibrium position.
A. 0.5 m/s
B. 1.0 m/s
C. 1.5 m/s
D. 2.0 m/s
Question 4
A projectile is launched from the ground with an initial velocity of 20 m/s at an angle of 60° above the horizontal. What is the maximum height reached by the projectile?
A. 10.0 m
B. 20.0 m
C. 30.0 m
D. 40.0 m
Question 5
A particle of mass 0.5 kg is attached to a spring with spring cons\tant 100 N/m. The particle is displaced by 0.2 m from its equilibrium position and released from rest. What is the angular frequency of the resulting simple harmonic motion?
A. 10 rad/s
B. 20 rad/s
C. 5 rad/s
D. 15 rad/s
Question 6
A quantum particle has a wave function given by \( \psi(x) = Ae^{-\alpha x^2} \). If the average value of the position of the particle is 0.5 m, calculate the value of the parameter \( \alpha \).
A. 0.01 m^{-2}
B. 0.05 m^{-2}
C. 0.10 m^{-2}
D. 0.20 m^{-2}
Question 7
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 8
A 50 Hz, 200 V AC supply is connected to a series RLC circuit with R = 10 Ω, L = 0.1 H, and C = 10 × 10^\( -6 \) F. The circuit has a phase angle of 30°. Calculate the impedance of the circuit.
A. ( 15.9 Omega )
B. ( 17.3 Omega )
C. ( 19.7 Omega )
D. ( 21.9 Omega )
Question 9
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. 2.5 m/s^2
B. 5.0 m/s^2
C. 7.5 m/s^2
D. 10.0 m/s^2
Question 10
A particle moves in a straight line with an initial velocity of 5 m/s and an acceleration of 2 m/s^2. Calculate the velocity of the particle after 4 seconds.
A. \( 9 , \text{m/s} \)
B. \( 10 , \text{m/s} \)
C. \( 11 , \text{m/s} \)
D. \( 12 , \text{m/s} \)
Question 11
A particle of mass 2.0 kg is moving in a circular path of radius 3.0 m with a cons\tant speed of 4.0 m/s. What is the magnitude of the net force acting on the particle?
A. 6.0 N
B. 12.0 N
C. 24.0 N
D. 48.0 N
Question 12
A magnetic field of 0.5 T is applied to a coil of 100 turns and a resis\tance of 10 Ω. Calculate the induced emf in the coil.
A. \( 5 , \text{V} \)
B. \( 10 , \text{V} \)
C. \( 15 , \text{V} \)
D. \( 20 , \text{V} \)
Question 13
A circuit consists of a resistor $R$ and an inductor $L$ connected in series. The circuit is driven by a voltage source $V_0$ with a frequency $f$. Find the impedance $Z$ of the circuit u\sing the formula $Z = \sqrt{R^2 + \( X_L - X_C \)^2}$, where $X_L = 2\pi f L$ and $X_C = \frac{1}{2\pi f C}$.
A. Z = \sqrt{R^2 + \( 2\pi f L \)^2}
B. Z = \sqrt{R^2 + \left\( \frac{1}{2\pi f C} \right \)^2}
C. Z = \sqrt{R^2 + \left\( 2\pi f L - \frac{1}{2\pi f C} \right \)^2}
D. Z = \sqrt{R^2 + \left\( 2\pi f L + \frac{1}{2\pi f C} \right \)^2}
Question 14
A heat engine operates between two reservoirs at temperatures 500 K and 300 K. If the engine absorbs 100 J of heat from the high-temperature reservoir, calculate the efficiency of the engine.
A. 0.25
B. 0.33
C. 0.40
D. 0.50
Question 15
A circuit consists of a 12 V battery, a 4 Ω resistor, and a 6 Ω resistor connected in parallel. What is the total resis\tance of the circuit?
A. 2.0 Ω
B. 4.0 Ω
C. 6.0 Ω
D. 8.0 Ω

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