A large number (n) of identical beads, each of mass m and radius r are strung on a thin smooth rigid horizontal rod of length `L (L gt gt r)` an dare at rest at random positions. The rod is mounted between two rigid supports (see figure). If one of the beads is now given a speed v, the average force experienced by each support after a lone time is (assume all collision are elastic) :-

Options

A. `(mv^(2))/(2 (L - nr))`
B. `(mv^(2))/(L - nr)`
C. zero
D. `(mv^(2))/(L - 2 nr)`

Answer

D

Explanation

Change In momentum in each collision with rigid support `DeltaP = 2mv`
time gap between two successive collision with same support `Deltat = (2L - 4nr)/(v)`
`F_("ave") = (DeltaP)/(Deltat)`