A stone is fastened to one end of a string and is whirled in a vertical circle of radius R. Find the minimum speed the stone can have at the highest point of the circle.

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where, m= mass of the stone


T=tension across the string


g=acceleration due to gravity


Centripetal force = mv2/r


At the highest point, mg + T = mv2/r


for speed, v to be minimum, T=0


⇒ mg = mv2/r


⇒ v2 = rg


⇒


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