The centripetal force acting on a body rotating in a circle of radius ‗r' is ‗F'. If the body moves in a circle of radius half of the initial value keeping other quantities constant, then the percentage change in the centripetal force is:
Correct answer: B. 100%
- A. 300%
- B. 100%
- C. 400%
- D. 200%
Explanation
To solve this problem, we start with the formula for centripetal force: F = (mv^2)/r.Initially, the force is F. When the radius is halved, the new radius is r/2. The new force becomes F' = (mv^2)/(r/2) = 2F.The percentage change in force is given by: [(F' - F) / F] × 100% = [(2F - F) / F] × 100% = 100%.Thus, the correct answer is 100%, which corresponds to Option B. Options A, C, and D represent incorrect calculations of the percentage change based on the new radius, leading to incorrect force changes.
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