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, 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_(1) and again at time t = T_(2). If .e. is the coefficient of restitution, find the ratio of T_(2)//T_(1)
Answer» Solution : `T_(1)=(PIR)/(u_1)"" ....(1)` `(v_(2)-v_(1))/(u_(1))=erArrv_(2)-v_(1)=eu_(1)` Time taken to COLLIDE A and B again, `T_(2)-T_(1)=(2piR)/(v_(2)-v_(1))rArrT_(2)-T_(1)=(2piR)/(eu_(1)) "" ....(2)` `(2)DIV(1)RARR(T_(2))/(T_(1))=(2+e)/(e)`