If the radius of a circular path is doubled while velocity stays the same, how does the centripetal force change?

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Multiple Choice

If the radius of a circular path is doubled while velocity stays the same, how does the centripetal force change?

Explanation:
For circular motion, the inward (centripetal) force is F = m v^2 / r. If you keep the speed the same and double the radius, that expression becomes F = m v^2 / (2r), which is half of the original. The centripetal acceleration is a_c = v^2 / r, so increasing the radius while keeping v fixed reduces the needed inward acceleration, and multiplying by mass gives the reduced force. Therefore, the centripetal force becomes half of what it was before.

For circular motion, the inward (centripetal) force is F = m v^2 / r. If you keep the speed the same and double the radius, that expression becomes F = m v^2 / (2r), which is half of the original. The centripetal acceleration is a_c = v^2 / r, so increasing the radius while keeping v fixed reduces the needed inward acceleration, and multiplying by mass gives the reduced force. Therefore, the centripetal force becomes half of what it was before.

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