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99 Percentile Qs Bank for JEE MainPhysicsCenter of Mass, Momentum and Collision

A ball is dropped from height H on to a horizontal surface. If the coefficient of restitution is e then the total time after which it comes to rest is

Options

  1. A2 H g 1 - e 1 + e
  2. B2 H g 1 + e 1 - e
  3. C2 H g 1 + e 2 1 - e 2
  4. D2 H g 1 - e 2 1 + e 2

Correct answer

B. 2 H g 1 + e 1 - e

Step-by-step solution

The time it takes for the ball to fall from a height is given by t = 2 H g The height up to which the ball bounces after the n th collision from the floor is H n = e 2 n H t = 2 H g + 2 2 H 1 g + 2 2 H 2 g + … ∞ t = 2 H g 1 + 2 e + 2 e 2 + … … . . ∞ t = 2 H g 1 + e 1 - e

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