Five identical balls each of mass m and radius r are string like beads at random and at rest along a smooth rigid horizontal thin rod of length L mounted between immovable supports Assume `10rleL` and that the collision between balls or between balls and supports are elastic if one ball is struck horizontally so as to acquire a speed v the average force felt by the support is

Options

A. `(5mv^(2))/(L-5r)`
B. `(mv^(2))/(L-10r)`
C. `(5mv^(2))/(L-10r)`
D. `(mv^(2))/(L-5r)`

Answer

B

Explanation

Total distance travelled by the successive balls balls for each pillar to be struck once is `d=2(L-10r)`
`time taken t=(2(L-10r))/v`
considering force on any one pillar
total change in momentium `=2mv`
`F_(avg)=(2mv)/t`
`(2mv^(2))/(2(L-10r))=(mv^(2))/(L-10r))`