question_answer

            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 (see figure). 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) : [JEE MAIN 11-04-2015]

A)  \[\frac{m{{\upsilon }^{2}}}{L-nr}\]     

B)       \[\frac{m{{\upsilon }^{2}}}{L-2nr}\]

C)  \[\frac{m{{\upsilon }^{2}}}{2(L-nr)}\]

D)        zero

Correct Answer: B

Solution :

[b] collisions are elastic and masses are equal, velocities of colliding particles get exchanged.

in each collision with the supports

Time interval between consecutive collisions with one support