A rubber ball is dropped from a height of `5m `on a plane, where the acceleration due to gravity is not shown. On bouncing it rises to `1.8 m.` The ball loses its velocity on bouncing by a factor of

Options

A. `16//25`
B. `2//5`
C. `3//5`
D. `9//25`

Answer

B

Explanation

If ball falls from height `h_(1)` and bounces back up to height `h_(2)` then `e= sqrt((h_(2))/(h_(1))`

Similarly if the velocity of ball before and after collision are `v_(1) and v_(2)` respectively then `e= (v_(2))/(v_(1))`
So `(v_(2))/(v_(1)) = sqrt((h_(2))/(h_(1))) = sqrt((1.8)/(5))= sqrt((9)/(25))= (3)/(5)`
i.e. fractional loss in velocity `=1-(v_(2))/(v_(1)) = 1- (3)/(5) = (2)/(5)`