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Question

Two small particles A & B of masses M and 2M respectively are joined rigidly to the ends of a light rod of length l as shown in the figure. The system translates on a smooth horizontal surface with a velocity u in a direction perpendicular to the rod. A particle P of mass M kept at rest on the surface sticks to the particle ‘A’ after collision with it. Then choose the correct option(s):


  1. The speed of particle A just after collision is u2 .

  2. The speed of particle B just after collision is u2 .

  3. The velocity of centre of mass of system A + B + P is 3u4

  4. The angular velocity of the system A + B + P after collision is u2l


Solution

The correct options are
A

The speed of particle A just after collision is u2 .


C

The velocity of centre of mass of system A + B + P is 3u4


D

The angular velocity of the system A + B + P after collision is u2l


By linear momentum conversation
M(u) + M(0) = (2M)v'
v=u2VCM=2M(u)+(2M)u24M=3u4ω=uu2l=u2l

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