A ball falls vertically onto a floor with momentum `p` and then bounces repeatedly. If coefficient of restitution is `e`, then the total momentum imparted by the ball to the floor is

Options

A. (a) `p(1+e)`
B. (b) `(p)/(1-e)`
C. (c) `p((1-e)/(1+e))`
D. (d) `p((1+e)/(1-e))`

Answer

D

Explanation

`DeltaP_1=(1+e)P`
`DeltaP_2=(1+e)eP`
and so on

`:. DeltaP_(Total)=DeltaP_1+DeltaP_2+…`
`=(1+e)P(1+e+e^2+…)`
`=((1+e)/(1-e))P`