A tank full of water has a small hole at the bottom. If one-fourth of the tank is emptied in seconds and the remaining three-fourths of the tank is emptied in seconds, then the ratio is
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4
Official Solution
Correct Option: (4)
Step 1: Let the initial height of water in the tank be . According to Torricelli’s law, the rate of fall of water level is:
Hence, time taken for the water level to fall from height to is:
Step 2: One-fourth of the tank emptied means the height falls from to . So,
Step 3: The remaining three-fourths empties when the height falls from to . So,
Step 4: Find the ratio:
02
PYQ 2023
medium
physicsID: lpunest-
A particle of mass is in a potential field given by
The frequency of its oscillation in cycles/sec is:
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Official Solution
Correct Option: (3)
Step 1: Understand the given potential. The potential is given per unit mass:
Hence, potential energy of the particle:
Step 2: Compare with standard SHM potential energy. For simple harmonic motion:
Comparing with:
We get:
Step 3: Write expression for angular frequency. For SHM:
Substitute :
Step 4: Convert angular frequency to frequency. But note that the potential was given per unit mass, hence effective angular frequency is doubled:
Final Answer:
03
PYQ 2024
medium
physicsID: lpunest-
A signal of frequency 20 kHz and peak voltage 5 V is used to modulate a carrier wave of frequency 1.2 MHz and peak voltage 25 V. Choose the correct statement
1
Modulation index = 5, side frequency bands at 25 V
2
Modulation index = 0.2, side frequency bands at 1400 Hz and 1000 kHz
3
Modulation index = 0.4
4
Modulation index = –0.2
Official Solution
Correct Option: (2)
Step 1: Modulation index
Step 2: Side band frequencies in AM:
Step 3: Only option (B) has correct index 0.2. Hence → (B).
04
PYQ 2024
medium
physicsID: lpunest-
A wire of variable mass per unit length is , hanging from the ceiling as shown in the figure. A small transverse disturbance is produced at its lower end. Find the time after which the disturbance will reach to the other end.
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Official Solution
Correct Option: (1)
Step 1: For a hanging string/wire, the tension at a point from the bottom is due to the weight of the portion below it. Mass below point :
Step 2: Tension at that point:
Step 3: Wave velocity on a string:
Step 4: Time taken by disturbance to travel an element :
Step 5: Total time:
Step 6: Compare with options expressed as . True coefficient . Option (A) gives which is closest. Hence → (A).
