Two identical 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 at time t = T, it impinges on sphere B. If e is the coefficient of restitution, the second impact will occur after a time equal to
If sphere A is projected with velocity v, time taken by it to strike B is equal to πrv=T⇒πr=Tv.
Now, the coefficient of restitution is given by e=vB−vAv where vA and vB are the velocities of A and B after the collision.
The spheres travel with this relative velocity. It is clear that one will overtake the other after travelling a distance 2πr.
∴ Time taken =2πrvB−vA=2πrev=2Tvev=2Te
Hence, the correct choice is (c).