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NTA Abhyas JEE Main2020PhysicsCenter of Mass, Momentum and CollisionPractice

A ball is dropped from height 5 m . What is the time (in seconds) after which ball stops rebounding if the coefficient of restitution between ball and ground e = 1 2 ?

Correct answer

3

Step-by-step solution

T = v g + 2 ev g + 2 e 2 v g + … … … ∞ T = v g 1 + 2 e + 2 e 2 + … … … ∞ T = v g 2 + 2 e + 2 e 2 + … … … ∞ - 1 T = v g 2 1 + e + e 2 + … … … ∞ - 1 T = v g 2 × 1 1 - e - 1       ⇒    T = 2 gh g 2 × 1 1 - 1 2 - 1          ⇒     T = 3 s

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