POST UTME IMS U 2023 Physics | Objective

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Question 1
A convex lens has a focal length of 0.2 m. What is the image dis\tance for an object placed 0.5 m from the lens?
A. 0.1 m
B. 0.2 m
C. 0.3 m
D. 0.4 m
Question 2
A 50 Hz AC voltage source is connected to a 100 Ω resistor in series with a 20 mH inductor. If the initial current is 0 A, find the current at t = 10 ms.
A. 0.5 A
B. 1.0 A
C. 1.5 A
D. 2.0 A
Question 3
A magnetic field of 0.1 T is applied to a current-carrying wire. What is the force on the wire if it carries a current of 2 A?
A. 0.2 N
B. 0.4 N
C. 0.6 N
D. 0.8 N
Question 4
A parallel plate capacitor has plates of area $A$ and separation $d$. If a dielectric slab of thickness $t$ and dielectric cons\tant $K$ is inserted between the plates, what is the new capaci\tance?
A. C' = \frac{KA}{d-t}\left\( 1-\frac{t}{d}\right \)
B. C' = \frac{KA}{d+t}\left\( 1+\frac{t}{d}\right \)
C. C' = \frac{KA}{d-t}\left\( 1+\frac{t}{d}\right \)
D. C' = \frac{KA}{d+t}\left\( 1-\frac{t}{d}\right \)
Question 5
A circuit consists of a 12 V battery, a 4 Ω resistor, and a 6 Ω resistor connected in series. What is the total resis\tance of the circuit?
A. 6 Ω
B. 8 Ω
C. 10 Ω
D. 12 Ω
Question 6
A heat engine operates between two temperatures $T_1$ and $T_2$. If the engine has an efficiency of $\eta$, what is the temperature of the hot reservoir?
A. \frac{T_1}{1-\eta}
B. \frac{T_2}{1-\eta}
C. \frac{T_1-T_2}{1-\eta}
D. \frac{T_1+T_2}{1-\eta}
Question 7
A particle of mass 2 kg is moving in a circular path with a radius of 3 m. If the particle's angular momentum is 6 kg m^2/s, what is its linear momentum?
A. 10 kg m/s
B. 12 kg m/s
C. 15 kg m/s
D. 20 kg m/s
Question 8
A 100 Hz AC voltage source is connected to a 50 Ω resistor in series with a 10 μF capacitor. If the initial current is 0 A, find the current at t = 5 ms.
A. 0.5 A
B. 1.0 A
C. 1.5 A
D. 2.0 A
Question 9
A radioactive sample has 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. 100 Bq
D. 200 Bq
Question 10
A thermodynamic system undergoes a process from state A to state B, where the internal energy (U) decreases by 100 J and the volume (V) increases by 0.1 m^3. If the pressure (P) remains cons\tant at 101325 Pa, what is the work done (W) by the system?
A. 1013.25 J
B. 1013.25 J
C. 1013.25 J
D. 1013.25 J
Question 11
A wave has a frequency of 50 Hz and a wavelength of 0.2 m. What is the speed of the wave?
A. 10 m/s
B. 100 m/s
C. 1000 m/s
D. 10000 m/s
Question 12
A sound wave has a frequency of $f$ and a speed of $v$. If the wave is reflected from a stationary surface, what is the frequency of the reflected wave?
A. f'
B. 2f'
C. f\left\( 1+\frac{v}{c}\right \)
D. f\left\( 1-\frac{v}{c}\right \)
Question 13
A container filled with water is 2 m tall and has a base area of 0.5 m^2. If the density of water is 1000 kg/m^3, calculate the pressure at the bottom of the container.
A. 9800 Pa
B. 19600 Pa
C. 29400 Pa
D. 39200 Pa
Question 14
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, find the speed of the block when it passes through its equilibrium position.
A. 0.5 m/s
B. 1.0 m/s
C. 1.5 m/s
D. 2.0 m/s
Question 15
A radioactive sample has a half-life of 10 years. If the initial activity is 1000 Bq, what is the activity after 20 years?
A. 125 Bq
B. 250 Bq
C. 500 Bq
D. 1000 Bq

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