POST UTME OSUSTECH 2023 Physics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A body is in equilibrium under the action of three forces: a 5 N force acting at an angle of 30° to the horizontal, a 10 N force acting at an angle of 60° to the horizontal, and a 15 N force acting at an angle of 90° to the horizontal. What is the resul\tant force acting on the body?
A. 10 N at an angle of 45° to the horizontal
B. 15 N at an angle of 30° to the horizontal
C. 20 N at an angle of 60° to the horizontal
D. 25 N at an angle of 90° to the horizontal
Question 2
A 2 kg block is attached to a horizontal, massless spring with a force cons\tant of 100 N/m. If the block is displaced by 0.2 m from its equilibrium position and released from rest, what is its maximum speed?
A. 2 m/s
B. 4 m/s
C. 6 m/s
D. 8 m/s
Question 3
A gas occupies a volume of 2 L at a pressure of 1 atm and a temperature of 300 K. If the pressure is increased to 2 atm, what is the new volume?
A. 1 L
B. 2 L
C. 4 L
D. 8 L
Question 4
A parallel plate capacitor has plates of area $A$ and separation $d$. The capacitor is connected to a battery of voltage $V$. Find the capaci\tance of the capacitor.
A. \frac{\epsilon_0 A}{d}
B. \frac{\epsilon_0 d}{A}
C. \frac{A}{\epsilon_0 d}
D. \frac{d}{\epsilon_0 A}
Question 5
A particle of mass 2 kg is attached to a spring with a spring cons\tant of 100 N/m. The particle is displaced by 0.2 m from its equilibrium position and released from rest. Assuming the motion is simple harmonic, calculate the maximum speed of the particle.
A. 2 m/s
B. 4 m/s
C. 6 m/s
D. 8 m/s
Question 6
A particle of mass $m$ is in a one-dimensional potential energy function $U(x) = \frac{1}{2}kx^2$. Assuming the particle is in a state of definite energy $E$, find the expectation value of the position $\langle x \rangle$ in terms of $k$, $E$, and $m$.
A. \langle x \rangle = \frac{E}{m}
B. \langle x \rangle = \frac{m}{k}
C. \langle x \rangle = \frac{E}{k}
D. \langle x \rangle = \frac{k}{E}
Question 7
A circuit consists of a resistor $R$, an inductor $L$, and a capacitor $C$ connected in series. The circuit is driven by an alternating voltage source of frequency $\omega$. Find 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{\( \omega L - \frac{1}{\omega C} \)^2 - R^2}
D. \sqrt{\( \omega L + \frac{1}{\omega C} \)^2 - R^2}
Question 8
A sound wave with a frequency of 200 Hz is traveling through a medium. If the speed of the sound wave is 340 m/s, what is the wavelength of the sound wave?
A. 1.7 m
B. 1.7 cm
C. 17 m
D. 17 cm
Question 9
A heat engine operates between two temperatures $T_1$ and $T_2$. The engine has an efficiency of $\eta$. Find the temperature of the hot reservoir.
A. 1 - \frac{T_2}{T_1}
B. \frac{T_2}{T_1}
C. T_1 - T_2
D. T_2 - T_1
Question 10
A 1000 W heater is used to heat a 5 kg block of copper from 20°C to 80°C. Assuming the specific heat capacity of copper is 0.385 J/g°C, calculate the energy required to heat the block to the desired temperature.
A. 2500 J
B. 5000 J
C. 7500 J
D. 10000 J
Question 11
A block of mass 5 kg is placed on a frictionless surface and attached to a horizontal spring with a force cons\tant of 200 N/m. If 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 12
A gas is compressed from an initial volume of $V_i$ to a final volume of $V_f$ at a cons\tant temperature of $T$. Assuming the gas obeys the ideal gas law, find the work done on the gas in terms of $p_i$, $V_i$, and $V_f$.
A. W = nRT \ln\left\( \frac{V_f}{V_i}\right \)
B. W = -nRT \ln\left\( \frac{V_i}{V_f}\right \)
C. W = nRT \ln\left\( \frac{V_i}{V_f}\right \)
D. W = -nRT \ln\left\( \frac{V_f}{V_i}\right \)
Question 13
A 5 kg block is pulled up a 2 m high incline with a force of 10 N. What is the work done on the block?
A. 20 J
B. 40 J
C. 60 J
D. 80 J
Question 14
A particle of mass $m$ is moving in a circular path of radius $r$ with a cons\tant speed $v$. Find the magnitude of the force acting on the particle.
A. \frac{mv^2}{r}
B. \frac{mr^2}{v}
C. \frac{v^2}{mr}
D. \frac{r}{mv^2}
Question 15
A body is in equilibrium under the action of two forces, one of 5 N and the other of 10 N. Calculate the angle between the forces.
A. 30°
B. 45°
C. 60°
D. 75°

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