POST UTME COAL CITY UNIVERSITY 2025 Physics | Objective

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Question 1
A thermodynamic system undergoes a process from an initial state (i) to a final state (f). The process is described by the equation \( Delta U = Q - W \), where ( Delta U ) is the change in internal energy, ( Q ) is the heat added to the system, and ( W ) is the work done by the system. If the system undergoes an isothermal expansion, what is the relationship between ( Q ) and ( W )?
A. Q = W
B. Q = -W
C. Q = 0
D. W = 0
Question 2
A particle of mass $m$ is projected from the origin with an initial velocity $v_0$ at an angle $\theta$ to the horizontal. Assuming the particle experiences a uniform gravitational field of strength $g$, determine the time $t$ at which the particle reaches its maximum height.
A. \frac{v_0 \sin \theta}{g}
B. \frac{v_0 \cos \theta}{g}
C. \frac{v_0 \sin \theta}{g^2}
D. \frac{v_0 \cos \theta}{g^2}
Question 3
A 10 Ω resistor is connected in series with a 20 Ω resistor and a 30 Ω resistor. What is the equivalent resis\tance of the circuit?
A. 20 Ω
B. 30 Ω
C. 40 Ω
D. 50 Ω
Question 4
A 2.5 mH inductor is connected in series with a 10 Ω resistor and a 12 V battery. If the switch is closed at t = 0, what is the current in the circuit at t = 10 ms?
A. 0.5 A
B. 1.0 A
C. 1.5 A
D. 2.0 A
Question 5
A gas of molecules with mass $m$ and charge $q$ is contained in a box of volume $V$. If the temperature of the gas is $T$, determine the average kinetic energy of the molecules.
A. \frac{3}{2} k_B T
B. \frac{1}{2} k_B T
C. k_B T
D. \frac{1}{2} m v^2
Question 6
A body is moving in a straight line with an initial velocity of 10 m/s and a uniform acceleration of 2 m/s^2. What is the velocity of the body after 5 seconds?
A. 10 m/s
B. 15 m/s
C. 20 m/s
D. 25 m/s
Question 7
A radioactive sample decays at a rate of 0.05% per hour. If the initial mass of the sample is 100 g, what is the mass of the sample after 5 hours?
A. 90.2 g
B. 92.3 g
C. 94.5 g
D. 96.7 g
Question 8
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. What is the magnitude of the force acting on the particle?
A. 10 N
B. 12 N
C. 14 N
D. 16 N
Question 9
A 10 Ω resistor is connected in series with a 20 Ω resistor. What is the equivalent resis\tance?
A. 10 Ω
B. 15 Ω
C. 20 Ω
D. 25 Ω
Question 10
A radioactive sample has a half-life of 5 years. If the initial activity of the sample is 1000 Bq, what is the activity of the sample after 10 years?
A. 250 Bq
B. 500 Bq
C. 750 Bq
D. 1000 Bq
Question 11
A series RLC circuit has a resis\tance of $R = 10\,\Omega$, an induc\tance of $L = 0.1\,H$, and a capaci\tance of $C = 10^{-6}\,F$. The circuit is driven by a \sinusoidal voltage source with a frequency of $f = 50\,Hz$. What is the impedance of the circuit?
A. 10\,\Omega
B. 20\,\Omega
C. 30\,\Omega
D. 40\,\Omega
Question 12
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. What is the magnitude of the force acting on the particle?
A. 8 N
B. 10 N
C. 12 N
D. 15 N
Question 13
A gas is confined to a container with a volume of $V = 10^{-3}\,m^3$. The gas is heated from an initial temperature of $T_1 = 300\,K$ to a final temperature of $T_2 = 400\,K$. Assuming the gas is ideal and the process is isobaric, what is the final volume of the gas?
A. 10^{-3}\,m^3
B. 2\times 10^{-3}\,m^3
C. 3\times 10^{-3}\,m^3
D. 4\times 10^{-3}\,m^3
Question 14
A magnetic field of 2 T is applied to a current-carrying wire of length 1 m. If the current in the wire is 5 A, what is the force experienced by the wire?
A. 10 N
B. 15 N
C. 20 N
D. 25 N
Question 15
A particle of mass ( m ) is confined to a one-dimensional box of length ( L ). The energy levels of the particle are given by the equation \( E_n = \frac{n^2 h^2}{8mL^2} \). If the particle is in the ground state, what is the energy of the particle?
A. \( \frac{h^2}{8mL^2} \)
B. \( \frac{h^2}{4mL^2} \)
C. \( \frac{h^2}{2mL^2} \)
D. \( \frac{h^2}{mL^2} \)

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