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Simple Harmonic Motion question

2002 · Shift 0 · Q155
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Simple Harmonic Motion question

2002 · Shift 0 · Q155

JEE MainPhysicsSimple Harmonic MotionMCQ+4 / −1
A child swinging on a swing in sitting position, stands up, then the time period of the swing will
  1. A
    increase
  2. B
    decrease
  3. C
    remains same
  4. D
    increases of the child is long and decreases if the child is short
View written solutionFree

Correct answer: B

  1. A swing behaves approximately like a pendulum.

  2. The time period of a pendulum is T=2πLgT = 2\pi\sqrt{\frac{L}{g}}T=2πgL​​ where:

    • LLL = effective length of the pendulum
    • ggg = acceleration due to gravity
  3. For a child on a swing, the effective length LLL is the distance from the point of suspension to the centre of mass of the child-swing system.

  4. When the child is in sitting position, the centre of mass is relatively lower.

  5. When the child stands up, the centre of mass moves upward, closer to the point of suspension. Therefore, the effective length LLL decreases.

  6. Since T∝L,T \propto \sqrt{L},T∝L​, a decrease in LLL causes the time period TTT to decrease.

  7. Hence, the correct option is: B: decrease\boxed{\text{B: decrease}}B: decrease​

Verification with stored answer

Stored correct answer: B

Our derived answer is also B, so they agree.

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