Q.

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

Moderate

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the momentum of the particle is shared between the particle and the rod and remains conserved.

the angular momentum about the mid-point of the rod before and after the collision is equal.

the angular momentum about the centre of mass of the combination before and after the collision is equal.

the centre of mass of the rod particle system starts to move translationally with the original momentum of the particle.

answer is 1,2,3,4.

(Detailed Solution Below)

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Detailed Solution

When the particle strikes at one end of the rod then an impulse is exerted by the particle on the rod along the direction of its original motion. An equal but opposite impulsive reaction is exerted by the rod on the particle. If system of rod and the particle is considered then there is no external impulse on the system, hence momentum of the system remains conserved. Hence, option (1) and 4 are correct.Since, both the impulsive reactions act at the same point, one acts on the rod and other on the particle, hence no angular impulse is produced by these impulsive reactions about any point. It means, angular momentum of the system remains conserved about every point. Hence, options (2) and (3) are correct.

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