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):

Question

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):, m v 2 L - n r, m v 2 L - 2 n r, m v 2 2 L - n r, Z e r o

MARKS App · Accepted Answer

Average time for 1 collision to occur on 1 wall, = t a v g = a v e r a g e d i s t a n c e t r a v e l l e d s p e e d = 2 L - 2 n r v ⇒ t a v g = 2 L - 2 n r v . Change in momentum in 1 collision = 2 m v . Average force on each support, f a v g = 2 m v t a v g = 2 m v 2 2 L - 2 n r ⇒ f a v g = m v 2 L - 2 n r .

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