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Question 30523
JEE Physics · Hard

Center of Mass, Momentum and Collision: Ballistic Pendulum MCQ

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Ballistic PendulumHardQuestion 30523

Question

A bullet (mass m, velocity v) embeds in a wooden block (mass M) hanging from strings of length L. The block+bullet swings up to height h. The bullet's initial velocity is:
  1. A
    (m+M)/m × √(2gh)
    Correct
  2. B
    m/(m+M) × √(2gh)
  3. C
    (M/m) × √(gh)
  4. D
    √(2gh)

Correct answer

(m+M)/m × √(2gh)

Explanation

Collision: mv = (m+M)v'. Then energy conservation: ½(m+M)v'² = (m+M)gh → v' = √(2gh). So v = (m+M)/m × √(2gh).

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