POST UTME BSU 2024 Physics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A ray of light passes from air into a glass slab of thickness $t$ and re\fractive index $n$. If the angle of incidence is $\theta_i$, what is the angle of re\fraction?
A. \frac{n\sin\theta_i}{n-\sin\theta_i}
B. \frac{n\sin\theta_i}{n+\sin\theta_i}
C. \frac{n\sin\theta_i}{n-\sin\theta_i}
D. \frac{n\sin\theta_i}{n+\sin\theta_i}
Question 2
A 100 Ω resistor is connected in series with a 20 μF capacitor and a 50 Hz AC source. What is the impedance of the circuit?
A. 100 Ω
B. 120 Ω
C. 140 Ω
D. 160 Ω
Question 3
A quantum particle has a wave function given by ( psi(x) = Ae^{-\alpha x^2} ). If the probability of finding the particle in the region \( -1 leq x leq 1 \) is 0.5, what is the value of the cons\tant \( \alpha \)?
A. 0.1
B. 0.2
C. 0.3
D. 0.4
Question 4
A circuit consists of a resistor $R$, an inductor $L$, and a capacitor $C$ connected in series. If the frequency of the AC source is $f$, what is the impedance of the circuit?
A. \sqrt{R^2+\( \omega L-\frac{1}{\omega C} \)^2}
B. \sqrt{R^2+\( \omega L+\frac{1}{\omega C} \)^2}
C. \sqrt{R^2+\( \omega L-\frac{1}{\omega C} \)^2}
D. \sqrt{R^2+\( \omega L+\frac{1}{\omega C} \)^2}
Question 5
A uniform magnetic field of strength 2 T is directed along the z-axis. A current of 5 A flows through a straight wire of length 0.5 m, placed along the x-axis. What is the magnitude of the magnetic force on the wire?
A. 0.5 N
B. 1 N
C. 2 N
D. 5 N
Question 6
A 50 Hz, 200 V AC supply is connected to a 100 Ω resistor. Calculate the rms value of the current flowing through the resistor.
A. 10 A
B. 14.14 A
C. 20 A
D. 28.28 A
Question 7
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. Calculate the magnitude of the force acting on the particle.
A. 10 N
B. 20 N
C. 30 N
D. 40 N
Question 8
A block of mass $m$ is attached to a horizontal, massless spring with a spring cons\tant $k$. The block is displaced by a dis\tance $x$ from its equilibrium position and released from rest. Assuming the block undergoes simple harmonic motion, what is the maximum speed $v_{max}$ of the block?
A. \sqrt{\frac{kx^2}{m}}
B. \sqrt{\frac{mx^2}{k}}
C. \sqrt{\frac{k}{m}}
D. \sqrt{\frac{m}{k}}
Question 9
A car travels from point A to point B with an average speed of $v_{avg}$. If the car takes a detour and travels from point A to point C to point B, the total dis\tance traveled is $d_{total}$. Assuming the car travels at a cons\tant speed of $v$ on the detour, what is the ratio of the average speed $v_{avg}$ to the speed $v$ on the detour?
A. \frac{v}{v_{avg}}
B. \frac{v_{avg}}{v}
C. \frac{d_{total}}{v}
D. \frac{v}{d_{total}}
Question 10
A radioactive sample decays at a rate given by 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 sample decays to $\frac{1}{4}$ of its initial value in $10$ years, what is the decay cons\tant $\lambda$?
A. \frac{1}{10}
B. \frac{1}{20}
C. \frac{1}{30}
D. \frac{1}{40}
Question 11
A magnetic field of strength 0.5 T is directed along the z-axis. A current of 2 A flows through a straight wire of length 1 m placed in the x-y plane. What is the magnitude of the magnetic force acting on the wire?
A. 0.1 N
B. 0.2 N
C. 0.3 N
D. 0.4 N
Question 12
A spring with a spring cons\tant of 100 N/m is stretched by 2 m. What is the potential energy stored in the spring?
A. 200 J
B. 400 J
C. 600 J
D. 800 J
Question 13
A quantum particle has a wave function given by \psi(x) = Ae^{-\alpha x^2}. What is the expectation value of the position operator?
A. 0
B. \frac{1}{\alpha}
C. \frac{1}{2\alpha}
D. \frac{1}{4\alpha}
Question 14
A radioactive sample decays with a half-life of 10 years. If the initial activity is 100 Bq, what is the activity after 20 years?
A. 25 Bq
B. 50 Bq
C. 75 Bq
D. 100 Bq
Question 15
A wave of wavelength $\lambda$ and frequency $f$ is traveling through a medium with a speed $v$. If the wave is reflected off a fixed \end and undergoes a phase shift of $\pi$, what is the new wavelength $\lambda_{new}$?
A. \lambda
B. \frac{\lambda}{2}
C. 2\lambda
D. \frac{\lambda}{4}

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