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. `p(1+e)`
B. `p/(1-e)`
C. `p(1+1/e)`
D. `p((1+e)/(1-e))`

Answer

D

Explanation

`/_\p=(p+ep)+(ep+e^(2)p)+(e^(2)p+e^(3)p)+`………..
`=p(1+e)[1+e+e^(2)+…..]=(p(1+e))/(1-e)`