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Two equal spheres A and B lie on a smoot...

Two equal spheres `A` and `B` lie on a smooth horizontal circular groove at opposite ends of a diameter. At time `t = 0`, A is projected along the groove and it first impinges on `B` at time `t = T_(1)` and again at time `t = T_(2)`. If `e` is the coefficient of restitution, the ratio `T_(2)//T_(1)` is

Text Solution

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The correct Answer is:
5

`T_(1)=(piR)/(u_(1))` .(1)
`e=(v_(2)-v_(1))/(u_(1))`
`T_(2)-T_(1)=(2piR)/(v_(2)-v_(1))implies(2piR)/(eu_(1))` .(2)
`(T_(2)-T_(1))/(T_(1))=(2)/(e)implies(T_(2))/(T_(1))=(2)/(e)+1=5`
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