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A particle is moving with uniform speed along the circumference of a circle of radius R under the action of a central fictitious force F which is inversely proportional to R³. Its time period of revolution will be given by:

1. T ∝ R²
2. T ∝ R^(3/2)
3. T ∝ R^(5/2)
4. T ∝ R^(4/3)

Correct answer: T ∝ R²

Solution

The time period of revolution for a particle moving in a circular path is related to the radius and the centripetal force acting on it. Since the fictitious force is inversely proportional to R³, the centripetal acceleration is proportional to F/R, leading to a relationship where the time period T is proportional to R².

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