POST UTME UI 2020 Physics | Objective

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Question 1
A particle of mass $m$ is confined to a one-dimensional box of length $L$. If the particle's wave function is given by $\psi(x) = A \sin \left\( \frac{n \pi x}{L} \right \)$, what is the value of the cons\tant $A$ in terms of $m$ and $L$?
A. \( A = \sqrt{\frac{2}{L}} \)
B. \( A = \sqrt{\frac{2 m}{L}} \)
C. \( A = \sqrt{\frac{2 L}{m}} \)
D. \( A = \sqrt{\frac{2 m L}{L}} \)
Question 2
A gas expands from an initial volume of 2 L to a final volume of 4 L against an external pressure of 1 atm. What is the work done by the gas?
A. 2 J
B. 4 J
C. 6 J
D. 8 J
Question 3
A block of mass 5 kg is attached to a spring with a spring cons\tant of 100 N/m. If the block is displaced by 0.2 m from its equilibrium position, what is the force exerted on the block?
A. -20 N
B. -10 N
C. 10 N
D. 20 N
Question 4
A gas is compressed adiabatically from an initial volume of 2 m^3 to a final volume of 1 m^3. If the initial temperature is 300 K, what is the final temperature?
A. 200 K
B. 250 K
C. 300 K
D. 350 K
Question 5
A block of mass 0.5 kg is attached to a spring with spring cons\tant 100 N/m. If the block is displaced by 0.1 m from its equilibrium position, calculate the potential energy stored in the spring.
A. 0.5 J
B. 1 J
C. 1.5 J
D. 2 J
Question 6
A spring with spring cons\tant $k$ is stretched by a dis\tance $x$ from its equilibrium position. If the force $F$ required to hold the spring in this position is given by Hooke's Law, what is the magnitude of the force $F$ in terms of $k$ and $x$?
A. \( F = k x \)
B. \( F = \frac{k x}{2} \)
C. \( F = k^2 x \)
D. \( F = \frac{k^2 x}{2} \)
Question 7
A circuit consists of a 2 Ω resistor and a 3 Ω resistor connected in parallel. If a voltage of 6 V is applied across the circuit, calculate the current through the 2 Ω resistor.
A. 1 A
B. 2 A
C. 3 A
D. 4 A
Question 8
A liquid with a density of 1000 kg/m^3 is flowing through a pipe with a radius of 0.1 m. If the pressure difference between the two \ends of the pipe is 1000 Pa, what is the velocity of the liquid?
A. 10 m/s
B. 20 m/s
C. 30 m/s
D. 40 m/s
Question 9
A sound wave with frequency $f$ and amplitude $A$ is propagating through a medium with speed $v$. If the wave's intensity is given by $I = \frac{P}{A}$, what is the value of the power $P$ in terms of $f$, $A$, and $v$?
A. \( P = \frac{A^2 f^2}{v} \)
B. \( P = \frac{A^2 f}{v} \)
C. \( P = \frac{A^2 f^2}{v^2} \)
D. \( P = \frac{A^2 f}{v^2} \)
Question 10
A particle of mass 2 kg is attached to a spring with spring cons\tant 100 N/m. It is displaced by 0.5 m from its equilibrium position and released from rest. Assuming the motion is simple harmonic, calculate the total energy of the particle after 2 seconds.
A. 10 J
B. 20 J
C. 30 J
D. 40 J
Question 11
A charged particle of mass $m$ and charge $q$ moves in a uniform magnetic field of strength $B$ with a velocity $v$. If the particle's trajectory is a circle of radius $r$, what is the magnitude of the magnetic field $B$ in terms of $m$, $q$, and $v$?
A. B = \frac{q^2}{4 \pi \epsilon_0 m v}
B. B = \frac{mv}{q r}
C. B = \frac{q r}{4 \pi \epsilon_0 m v}
D. B = \frac{q^2}{4 \pi \epsilon_0 m v^2}
Question 12
A convex lens of focal length 20 cm is used to form an image of an object placed 30 cm in front of it. What is the magnification of the image?
A. -1
B. -2
C. -3
D. -4
Question 13
A photon of wavelength 400 nm is incident on a metal surface. If the work function of the metal is 2.5 eV, what is the maximum kinetic energy of the emitted electron?
A. 1.5 eV
B. 2.5 eV
C. 3.5 eV
D. 4.5 eV
Question 14
A 10 μF capacitor is connected in parallel with a 20 μF capacitor. What is the equivalent capaci\tance?
A. 10 μF
B. 20 μF
C. 30 μF
D. 40 μF
Question 15
A 5 kg block is moving with a velocity of 2 m/s. What is its kinetic energy?
A. 5 J
B. 10 J
C. 15 J
D. 20 J

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