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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


  1. the velocity of B immediately after impact is V0
  2. the velocity of C when the stretch in the spring is maximum is 2v05
  3. the velocity of B when the stretch in the spring is maximum is 4v05
  4. the 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 m5kv0
At 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

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