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 $L ( L \gg r )$ 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): (1) $\frac { m v ^ { 2 } } { L - n r }$ (2) $\frac { m v ^ { 2 } } { L - 2 n r }$ (3) $\frac { m v ^ { 2 } } { 2 ( L - n r ) }$ (4) Zero
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 $L ( L \gg r )$ 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):\\
(1) $\frac { m v ^ { 2 } } { L - n r }$\\
(2) $\frac { m v ^ { 2 } } { L - 2 n r }$\\
(3) $\frac { m v ^ { 2 } } { 2 ( L - n r ) }$\\
(4) Zero