A ball of mass m is dropped onto a floor from a certain height. The collision is perfectly elastic and the ball rebounds to the same height and again falls. Find the averge force exerted by the ball on the floor during a long time interval.

Options

A. `2 mg`
B. `mg`
C. `3 mg`
D. `4 mg`

Answer

B

Explanation

During one collision
`(Delta p)_(ball) = [mv - (-mv)] = 2mv = 2m sqrt(2gh)`
Time of fall of the ball `= t_(0) = sqrt((2h)/(g))`
Time taken by the fall in successive collision `= 2 t_(0)`
Average force `= (Delta p)/(Delta t) = (2m sqrt( 2 gh))/(2t_(0) = 2 sqrt((2h)/(g)))`