  Question

# Three particles each of mass m, can slide on fixed frictionless circular tracks in the same horizontal plane as shown. Particle A moves with velocity V0 and hits particle B elastically. Assuming that B and C are initially at rest and lie along a radial line and the spring is initially relaxed before impact, then the velocity of B immediately after impact is V0the velocity of C when the stretch in the spring is maximum is 2v05the velocity of B when the stretch in the spring is maximum is 4v05the maximum stretch in the spring in the spring is √m5kv0

Solution

## The correct options are A the velocity of B immediately after impact is V0 B the velocity of C when the stretch in the spring is maximum is 2v05 C the velocity of B when the stretch in the spring is maximum is 4v05 D the maximum stretch in the spring in the spring is √m5kv0At the time of maximum elongation angular speed of B and C are equal, let speed of B is 2v and C is v, By conserving angular momentum of the system about the centre mv0 2R=m2v (2R)+mv (R) v=2v05,            vB=4v05,            vc=2v05 Conserving energy of the system 12mv20=12kx2max+12m(4v05)2+12m(2v05)2 ∴        xmax=√m5kv0  Suggest corrections   