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

• A
  $\frac{mv^2}{2(L - nr)}$
• B
  $\frac{mv^2}{L - 2nr}$
• C
  $\frac{mv^2}{L - nr}$
• D
  zero