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Periodic Motion

A ball is dro...

Question

A ball is dropped from height $h$ on a horizontal floor. If it loses $60 %$ of its energy on hitting the floor, find the height to which it will rise.

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Solution

Initial energy = PE = mgh
On losing $60 %$ energy, energy left = mgh - $\frac{60}{100}$ mgh = 0.4 mgh
Let the height upto which it will bounce be h'.
So, 0.4 mgh = mgh'
$\Rightarrow$ h' = 0.4 h = $\frac{2}{5} h$

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