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In a circus, a stuntman rides a motorbike on a circular track of radius \(R\) in the vertical plane. The minimum speed at the highest point of the track is:

1. 2gR
2. 2gR
3. 3gR
4. gR

Correct answer: 2gR

Solution

For the minimum speed at the top of a vertical loop, the bike just maintains contact, so normal reaction is zero. Then gravity alone provides centripetal force: \(mg = mv^2/R\), giving \(v = \sqrt{gR}\).

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