POST UTME BSU 2017 Physics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A solid cylindrical block of wood with a radius of 5 cm and a height of 10 cm is floating in water. If the density of the wood is 0.6 g/cm³, what is the percentage of the volume of the wood that is submerged in water?
A. 20%
B. 30%
C. 40%
D. 50%
Question 2
A radioactive sample decays according to the equation $N(t) = N_0 e^{-lambda t}$, where $N(t)$ is the number of nuclei remaining at time $t$, $N_0$ is the initial number of nuclei, and $lambda$ is the decay cons\tant. If the half-life of the sample is $10,mathrm{years}$, calculate the decay cons\tant $lambda$.
A. \( lambda = \frac{ln 2}{10} \)
B. \( lambda = \frac{10}{ln 2} \)
C. \( lambda = \frac{2}{10} \)
D. \( lambda = \frac{10}{2} \)
Question 3
A s\tanding wave is formed on a string of length 1 m with a frequency of 50 Hz. If the string is fixed at both \ends, calculate the wavelength of the wave.
A. 0.04 m
B. 0.08 m
C. 0.12 m
D. 0.16 m
Question 4
A ray of light passes from air into a glass slab of thickness $t = 0.5, \text{m}$ and re\fractive index $n = 1.5$. If the angle of incidence is $\theta_i = 30^\circ$, what is the angle of re\fraction?
A. 20^\circ
B. 30^\circ
C. 40^\circ
D. 50^\circ
Question 5
A block of mass 5 kg is attached to a horizontal, massless spring with a force cons\tant of 200 N/m. The block is displaced by 2 m from its equilibrium position and released from rest. What is the maximum speed of the block?
A. 2 m/s
B. 4 m/s
C. 6 m/s
D. 8 m/s
Question 6
A gas at a pressure of 1 atm and a temperature of 300 K is compressed to a pressure of 2 atm and a temperature of 400 K. What is the new volume of the gas?
A. 0.5 L
B. 1 L
C. 2 L
D. 4 L
Question 7
A parallel plate capacitor has plates of area 0.04 m^2 and separation 0.02 m. If the dielectric cons\tant of the material between the plates is 3.2, calculate the capaci\tance.
A. 1.6 x 10^-10 F
B. 3.2 x 10^-10 F
C. 4.8 x 10^-10 F
D. 6.4 x 10^-10 F
Question 8
A particle of mass $m$ is projected from the origin with an initial velocity $mathbf{v}_0 = v_0 \cos \theta mathbf{i} + v_0 \sin \theta mathbf{j}$, where $v_0$ is the magnitude of the initial velocity and $\theta$ is the angle of projection. If the particle is subject to a uniform gravitational field of strength $g$, find the equation of the trajectory of the particle in the $xy$-plane.
A. \( y = \frac{v_0^2}{2g} \sin^2 \theta - \frac{gx^2}{2v_0^2 \cos^2 \theta} \)
B. \( y = \frac{v_0^2}{2g} \sin^2 \theta + \frac{gx^2}{2v_0^2 \cos^2 \theta} \)
C. \( y = \frac{v_0^2}{2g} \sin^2 \theta - \frac{gx^2}{2v_0^2 \cos^2 \theta} + \frac{v_0^2}{2g} \)
D. \( y = \frac{v_0^2}{2g} \sin^2 \theta + \frac{gx^2}{2v_0^2 \cos^2 \theta} - \frac{v_0^2}{2g} \)
Question 9
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. 0
B. \frac{L}{2}
C. L
D. \frac{L}{4}
Question 10
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. 12 m/s^2
C. 18 m/s^2
D. 24 m/s^2
Question 11
A photon of energy $E = hf$ is incident on a metal surface. If the work function of the metal is $W = hf_0$, calculate the maximum kinetic energy of the electron emitted.
A. \( E - W \)
B. \( E + W \)
C. \( E - W + hf \)
D. \( E + W - hf \)
Question 12
A 100 W light bulb is connected to a 220 V power source. If the resis\tance of the light bulb is 100 Ω, what is the current flowing through the light bulb?
A. 0.5 A
B. 1 A
C. 2 A
D. 4 A
Question 13
A 10 μC point charge is placed at the center of a circular loop of radius 0.5 m. The loop has a resis\tance of 5 Ω and an induc\tance of 0.2 H. What is the magnitude of the current in the loop 0.1 s after the charge is placed?
A. 0.2 A
B. 0.4 A
C. 0.6 A
D. 0.8 A
Question 14
A gas at 300 K and 1 atm expands to 2 atm at cons\tant temperature. What is the final volume of the gas?
A. 1.5 L
B. 2.0 L
C. 2.5 L
D. 3.0 L
Question 15
A 10 kg block of copper is heated from 20°C to 80°C. If the specific heat capacity of copper is 0.385 J/g°C, what is the energy transferred to the block?
A. 38.5 J
B. 385 J
C. 3850 J
D. 38500 J

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