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Objective Type Questions – SHM (Page 8)
Type: Tough Numerical & Multi-Concept
Difficulty: JEE Advanced
Instructions:
Each question has one correct option. Calculations may involve energy, phase, graphs, and limiting conditions.
Each question has one correct option. Calculations may involve energy, phase, graphs, and limiting conditions.
Q71.
A particle executes SHM with amplitude A and angular frequency ω. At what displacement from mean position will its speed be half of the maximum speed?
Answer: √3A/2
Tip: Use v = ω√(A² − x²)
A particle executes SHM with amplitude A and angular frequency ω. At what displacement from mean position will its speed be half of the maximum speed?
Answer: √3A/2
Tip: Use v = ω√(A² − x²)
Q72.
The ratio of kinetic energy to potential energy of a particle in SHM is 3. Find the displacement in terms of amplitude A.
Answer: x = A/2
Trick: KE/PE = (A² − x²)/x²
The ratio of kinetic energy to potential energy of a particle in SHM is 3. Find the displacement in terms of amplitude A.
Answer: x = A/2
Trick: KE/PE = (A² − x²)/x²
Q73.
A particle in SHM spends maximum time near:
(A) Mean position
(B) Extreme position
(C) Half amplitude
(D) Everywhere equally
Correct Answer: B
Reason: Velocity is minimum near extremes
A particle in SHM spends maximum time near:
(A) Mean position
(B) Extreme position
(C) Half amplitude
(D) Everywhere equally
Correct Answer: B
Reason: Velocity is minimum near extremes
Q74.
If the total energy of an SHM particle is E, its kinetic energy at displacement x is:
Answer: E(1 − x²/A²)
If the total energy of an SHM particle is E, its kinetic energy at displacement x is:
Answer: E(1 − x²/A²)
Q75.
The time taken by a particle to move from x = A/2 to x = A is:
Answer: T/6
Method: Use phase difference (sin⁻¹ rule)
The time taken by a particle to move from x = A/2 to x = A is:
Answer: T/6
Method: Use phase difference (sin⁻¹ rule)
Q76.
In SHM, acceleration is equal in magnitude at two points x₁ and x₂. Then:
Answer: x₁ = ±x₂
In SHM, acceleration is equal in magnitude at two points x₁ and x₂. Then:
Answer: x₁ = ±x₂
Q77.
A mass attached to a spring performs SHM. If mass is doubled, time period becomes:
Answer: √2 times
A mass attached to a spring performs SHM. If mass is doubled, time period becomes:
Answer: √2 times
Q78.
For a particle executing SHM, maximum acceleration is:
Answer: ω²A
For a particle executing SHM, maximum acceleration is:
Answer: ω²A
Q79.
If displacement in SHM is doubled, restoring force becomes:
Answer: Doubled
If displacement in SHM is doubled, restoring force becomes:
Answer: Doubled
Q80.
Which quantity remains constant throughout SHM?
(A) Velocity
(B) Acceleration
(C) Total Energy
(D) Momentum
Correct Answer: C
Which quantity remains constant throughout SHM?
(A) Velocity
(B) Acceleration
(C) Total Energy
(D) Momentum
Correct Answer: C
End of Objective Page 8
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