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, and again at time t = T_(1)Ife is the coefficient of restitution, find the ratio of T _(2) //T_(1).

Two equal spheres A and B lie on a smooth horizontal circular groove a

1.	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, and again at time t = T_(1)Ife is the coefficient of restitution, find the ratio of T _(2) //T_(1).
Answer» SOLUTION : `T _(1) = (pi R )/( u _(1)) ""...(1)` `(v _(2) - v _(1))/(u _(1)) = e implies v _(2) - v _(1) = EU _(1)` .A. makes `2^(nd)` impact with B when B travels a distance `2pi R` as SEEN by A after `1 ^(st)` impact. TIME taken to collide A and B again: `T _(2) - T _(1) = (2pi R )/( v _(2) - v _(1)) implies T _(2) - T _(1) = (2pi R )/( eu _(1)) ...(2)` `(2)div(1) implies(T _(2))/( T _(1)) = (2 + e )/( e)`