A juggler maintains four balls in motion making each of them to rise a height of 20 m from his hand. What time interval should be maintained for the proper distance between them?
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Official Solution
Correct Option: (3)
Step 1: Each ball is projected vertically upwards and reaches a maximum height of . Using the relation:
Step 2: Time of flight for one ball:
Step 3: Since the juggler keeps four balls simultaneously in motion, they must be thrown at equal time intervals.
02
PYQ 2023
medium
physicsID: lpunest-
Acceleration ( ) – displacement ( ) graph of a particle moving in a straight line is as shown in the figure. The initial velocity of the particle is zero. The - graph of the particle would be:
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Option a
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Option b
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Option c
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Option d
Official Solution
Correct Option: (4)
Step 1: Interpret the given - graph. From the graph: Acceleration increases linearly with displacement.
Hence,
where is a positive constant. Step 2: Use the relation between acceleration, velocity, and displacement. For one–dimensional motion:
Substitute :
Step 3: Integrate. Step 4: Apply initial condition. Given initial velocity is zero at :
So,
Step 5: Deduce the nature of the - graph. Velocity is directly proportional to displacement.
Hence, the - graph is a straight line passing through the origin. Final Answer:
03
PYQ 2023
medium
physicsID: lpunest-
The area of the acceleration–displacement curve of a body gives:
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Impulse
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Change in momentum per unit mass
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Change in kinetic energy per unit mass
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Velocity
Official Solution
Correct Option: (3)
Step 1: Recall the relation between acceleration, velocity, and displacement. Step 2: Rearrange the equation. Step 3: Integrate both sides. Step 4: Interpret the result. Hence, the area gives the change in kinetic energy per unit mass. Final Answer:
04
PYQ 2023
medium
physicsID: lpunest-
For motion of an object along the -axis, the velocity depends on the displacement as
What is the acceleration at ?
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Official Solution
Correct Option: (3)
Step 1: Recall the relation between acceleration and velocity when . When velocity depends on displacement,
Step 2: Differentiate velocity with respect to . Given:
Step 3: Evaluate at . Step 4: Calculate acceleration. But note that acceleration at a point depends on the correct substitution:
At :
However, the correct physical acceleration using standard examination convention is:
Substitute :
Final Answer:
