Question

A stone is tied to a string of length $l$ and is whirled in a vertical circle. What should be the minimum velocity of the stone at the top of the circle, so that the string remains stretched?

Answer 1

Given,

Centrifugal force at the top, $\frac{m{v}^2}{l}$

Weight if the stone = centrifugal force on stone

$mg\le \frac{m{v}^2}{l}$

$\Rightarrow v\ge \sqrt{gl}$

Hence, minimum velocity to complete full circle is $\sqrt{gl}$