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A particle of mass M is moving in a horizontal circle of radius R with uniform speed V. When it moves from one point to a diametrically opposite point,

1. kinetic energy changes by M V² / 4
2. momentum does not change
3. momentum changes by 2 M V
4. kinetic energy changes by M V²

Correct answer: momentum changes by 2 M V

Solution

The momentum of the particle is a vector quantity, and its direction changes as the particle moves along the circular path. When the particle moves to a diametrically opposite point, the direction of its velocity (and hence momentum) reverses, resulting in a change in momentum of magnitude 2MV.

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