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.
This question appeared on the ETEA MDCAT 2012 paper, which you can sit online with every answer explained.
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About Angular and Linear Quantities
Rotational motion relates angular displacement, angular velocity and angular acceleration to linear displacement, tangential velocity and tangential acceleration through the radius. Questions use radians, v equals r omega and tangential acceleration, while distinguishing tangential velocity from centripetal acceleration and angular quantities from their linear counterparts.
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