POST UTME REDEEMERS UNIVERSITY 2021 Physics | Objective

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 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. nL/\pi
C. L/\pi
D. nL/2\pi
Question 2
A heat engine operates between the temperatures 500 K and 300 K. If the heat engine absorbs 1000 J of heat from the high-temperature reservoir, what is the efficiency of the engine?
A. 0.25
B. 0.30
C. 0.35
D. 0.40
Question 3
A 100 V AC supply is connected to a 50 Ω resistor. If the current is 2 A, what is the power factor?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 4
A 100 W heater is connected to a 230 V AC supply. If the current is 0.5 A, what is the power factor?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 5
A particle of mass $m$ is confined to a one-dimensional box of length $L$. If the particle is in the ground state, what is the expectation value of its position?
A. \frac{L}{2}
B. \frac{L}{4}
C. \frac{3L}{4}
D. \frac{L}{4}
Question 6
A wave of frequency $f$ and wavelength $lambda$ is traveling through a medium with speed $v$. What is the angular frequency of the wave?
A. ( 2pi f )
B. \( \frac{2pi f}{lambda} \)
C. \( \frac{lambda}{2pi f} \)
D. \( \frac{v}{2pi f} \)
Question 7
A body of mass 2 kg is moving in a circular path of radius 3 m with a cons\tant speed of 4 m/s. What is the magnitude of the force acting on the body?
A. 10 N
B. 20 N
C. 30 N
D. 40 N
Question 8
A block of mass $M$ is placed on a frictionless surface and connected to a horizontal spring with spring cons\tant $k$. The block is displaced by a dis\tance $x$ and released from rest. What is the angular frequency of the resulting simple harmonic motion?
A. \sqrt{k/M}
B. k/M
C. 2\sqrt{k/M}
D. M/k
Question 9
A charged particle of mass $m$ and charge $q$ is moving in a uniform magnetic field $\vec{B}$. If the particle is moving in a circular path of radius $R$, what is the speed of the particle?
A. \frac{qBR}{m}
B. \frac{qB}{m}
C. \frac{m}{qB}
D. \frac{q}{mB}
Question 10
A 2.5 m long wire is made of a material with a resistivity of 2.1 × 10^\( -8 \) Ωm. If the wire is stretched to a length of 5 m, what is the new resis\tance?
A. 1.05 × 10^\( -7 \) Ω
B. 2.1 × 10^\( -7 \) Ω
C. 4.2 × 10^\( -7 \) Ω
D. 5.25 × 10^\( -7 \) Ω
Question 11
A 100 V, 50 Hz AC supply is connected to a 50 Ω resistor. What is the rms value of the current flowing through the resistor?
A. 1 A
B. 2 A
C. 5 A
D. 10 A
Question 12
A 10 Ω resistor is connected in parallel with a 20 Ω resistor. What is the equivalent resis\tance?
A. 5 Ω
B. 10 Ω
C. 15 Ω
D. 20 Ω
Question 13
A block of mass $M$ is placed on a frictionless surface and attached to a horizontal spring with spring cons\tant $k$. The block is displaced by a dis\tance $x$ from its equilibrium position and released from rest. What is the angular frequency of the resulting simple harmonic motion?
A. \( \sqrt{\frac{k}{M}} \)
B. \( \frac{k}{M} \)
C. \( \frac{M}{k} \)
D. \( \frac{2k}{M} \)
Question 14
A particle of mass 2 kg is moving in a circular path with a radius of 3 m. If the particle has a speed of 4 m/s, what is its kinetic energy?
A. 10 J
B. 20 J
C. 30 J
D. 40 J
Question 15
A projectile is launched from the origin with an initial velocity $v_0$ at an angle $\theta$ above the horizontal. What is the maximum height reached by the projectile?
A. \( \frac{v_0^2 \sin^2 \theta}{2g} \)
B. \( \frac{v_0^2 \cos^2 \theta}{2g} \)
C. \( \frac{v_0^2 \sin \theta}{2g} \)
D. \( \frac{v_0^2 \cos \theta}{2g} \)

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