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A uniform rod is resting freely over a smooth horizontal plane. A particle moving horizontally strikes at one end of the rod normally and gets stuck. Then This question has multiple correct options

1. the momentum of the particle is shared between the particle and the rod and remains conserved
2. the angular momentum about the mid-point of the rod before and after the collision is equal
3. the angular momentum about the centre of mass of the combination before and after the collision is equal
4. the centre of mass of the rod particle system starts to move translationally with the original momentum of the particle

Correct answer: the momentum of the particle is shared between the particle and the rod and remains conserved

Solution

The particle sticks to the rod, so the collision is perfectly inelastic, but the plane is smooth and cannot provide horizontal impulse. Therefore the total linear momentum of the particle-rod system is conserved, and that momentum is shared by both bodies after impact. Angular momentum depends on the chosen point, so it is not automatically conserved about arbitrary points like the rod’s midpoint.

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