POST UTME ELIZADE UNIVERSITY 2017 Physics | Objective

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Question 1
A particle of mass $m$ is in a one-dimensional potential well of depth $V_0$. Assuming the particle is in the ground state, find the energy of the particle.
A. \frac{\hbar^2}{2m} \left\( \frac{\pi}{L} \right \)^2
B. \frac{\hbar^2}{2m} \left\( \frac{2\pi}{L} \right \)^2
C. \frac{\hbar^2}{2m} \left\( \frac{3\pi}{L} \right \)^2
D. \frac{\hbar^2}{2m} \left\( \frac{4\pi}{L} \right \)^2
Question 2
A convex lens of focal length 20 cm is used to form an image of an object placed 30 cm in front of it. Calculate the magnification of the image.
A. 0.5
B. 1
C. 2
D. 3
Question 3
A ray of light passes from air into a glass of re\fractive index 1.5. If the angle of incidence is 30°, calculate the angle of re\fraction u\sing Snell's law.
A. 20°
B. 25°
C. 30°
D. 35°
Question 4
A block of mass 2 kg is attached to a horizontal spring with a spring cons\tant of 100 N/m. If the block is displaced by 0.2 m from its equilibrium position and released from rest, calculate the maximum velocity of the block u\sing the equation for simple harmonic motion.
A. 0.2 m/s
B. 0.4 m/s
C. 0.6 m/s
D. 0.8 m/s
Question 5
A radioactive sample decays at a rate proportional to its current mass. Which of the following statements is true about the decay rate?
A. The decay rate is cons\tant.
B. The decay rate is proportional to the current mass.
C. The decay rate is inversely proportional to the current mass.
D. The decay rate is indep\endent of the current mass.
Question 6
A capacitor consists of two parallel plates separated by a dis\tance $d$. The plates have a charge $Q$ and a capaci\tance $C$. Assuming the electric field between the plates is uniform, find the potential difference between the plates.
A. \frac{Q}{C}
B. \frac{C}{Q}
C. \frac{d}{C}
D. \frac{C}{d}
Question 7
A projectile is launched at an angle of 30° to the horizontal with an initial velocity of 20 m/s. If the air resis\tance is negligible, what is the maximum height reached by the projectile?
A. 10 m
B. 20 m
C. 30 m
D. 40 m
Question 8
A particle of mass 2 kg is attached to a spring with spring cons\tant 100 N/m. It is displaced by 0.2 m from its equilibrium position and released from rest. Assuming the motion is simple harmonic, calculate the time taken for the particle to reach its maximum speed.
A. 0.1 s
B. 0.2 s
C. 0.5 s
D. 1 s
Question 9
A parallel plate capacitor has a capaci\tance of 10 μF and is charged to a potential difference of 100 V. If the dis\tance between the plates is doubled, what is the new capaci\tance?
A. 5 μF
B. 10 μF
C. 20 μF
D. 40 μF
Question 10
A beam of light passes through a prism and is re\fracted. The angle of incidence is $i$ and the angle of re\fraction is $r$. Assuming the prism is made of glass with a re\fractive index $n$, find the angle of deviation.
A. \( n-1 \)\( i-r \)
B. \( n-1 \)\( i+r \)
C. \( n+1 \)\( i-r \)
D. \( n+1 \)\( i+r \)
Question 11
A magnetic field is generated by a current-carrying wire. Which of the following statements is true about the direction of the magnetic field?
A. The magnetic field lines are parallel to the wire.
B. The magnetic field lines are perp\endicular to the wire.
C. The magnetic field lines are at an angle to the wire.
D. The magnetic field lines are circular around the wire.
Question 12
A particle of mass $m$ is attached to a spring with spring cons\tant $k$. The particle is displaced from its equilibrium position by a dis\tance $x_0$ and released from rest. Assuming the motion is simple harmonic, find the angular frequency of the particle's motion.
A. \sqrt{\frac{k}{m}}
B. \frac{k}{m}
C. \frac{m}{k}
D. \frac{1}{\sqrt{mk}}
Question 13
A wave has a frequency of 50 Hz and a wavelength of 2 m. If the wave is traveling in the positive x-direction, what is the direction of the group velocity?
A. Positive x-direction
B. Negative x-direction
C. Positive y-direction
D. Negative y-direction
Question 14
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. If the particle is subjected to a centripetal force of 12 N, what is the magnitude of the acceleration of the particle?
A. 6 m/s^2
B. 8 m/s^2
C. 10 m/s^2
D. 12 m/s^2
Question 15
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. -0.5
B. -1
C. -1.5
D. -2

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