A large number (n) of identical beads,each of | vedclass

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(B) The total length available for the motion of the beads is $L_{eff} = L - 2nr$,as each of the $n$ beads occupies a length of $2r$. When a bead move

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$\frac{mv^2}{L - 2nr}$

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(B) The total length available for the motion of the beads is $L_{eff} = L - 2nr$,as each of the $n$ beads occupies a length of $2r$. When a bead moves with speed $v$ and undergoes elastic collisions with the supports,the change in momentum for one collision with a support is $\Delta p = mv - (-mv) = 2mv$. The time taken to travel between the two supports and return is $\Delta t = \frac{2(L - 2nr)}{v}$. The average force $F$ exerted on each support is given by the rate of change of momentum: $F = \frac{\Delta p}{\Delta t} = \frac{2mv}{2(L - 2nr) / v} = \frac{mv^2}{L - 2nr}$.

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