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

Answer

C

Explanation

When a particle undergoes normal collision with a floor or a wall, with coefficient of restitution `e`, the speed after collision is `e` times the speed before collision. Therefore, change in momentum after first impact `= ep-(-p) =p(1+e)`
After the second impact, change in momentum would be `e(ep)-(-ep)=ep(1+e)` and so on. ltbr. Therefore, total change in momentum of ball
`=` momentum imparted to floor
`=p(1+e) [1+e+e^(2)+......]`
`[p(1+e)[(1)/(1-e)]=(p(1+e))/((1-e)) `