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Two equal sphere A and b lie on a smooth...

Two equal sphere `A and b` lie on a smooth horizontal circle groove at opposite ends of a diameter. At time `t= 0,A` is projected along the groove and tis first implings 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

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`T_(1) = (pi R)/(u_(1)` ….(1)
`(v_(2)-v_(1))/(u_(1)) =e rArr v_(2) -v_(1) = eu_(1)`
Time taken for `A` to collide with `B` again us
`T_(2)-T_(1)=(2pi R)/(v_(2)-v_(1)) rArr T_(2)-T_(1) =(2 piR)/(eu_(1))` ….(2)
from (1) and (2), `(T_(2))/(T_(1)) = (2+e)/( e)`.
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