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 support (see fig) . If one of the beat is now given a speed v, the average force experienced by each support after a long time is (assume all collision are elastic ):

Question

$\begin{array}{1 1} \frac{mv^2}{L-nr} \\\frac{mv^2}{L-2nr} \\ \frac{mv^2}{2(L-nr)} \\ zero \end{array} $