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Question

In the pulleys system as shown in the figure a particle of mass m falls from a height h0 on the mass m and gets stuck to it. Speed with which the system moves just after the collision is:


  1. 2gh04
  2. 2gh0
  3. gh02
  4. 2gh05


Solution

The correct option is D 2gh05
For collision process, COM gives
mu=2mv0v0=v2
where, u=2gh0
Just after collisions, one can conserve angular momentum about the centre of the pulley.
COAM
Li=Lf
2mv0R=2mvR+3mvR
Where R: radius of the pulley
V: final velocities of m and 3m
v=2V05
=25×2gh02
=2gh05

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