Question

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.

Answer 1

The force acting on the body moving in a circle is centrifugal which is given as

$F_c=\frac{m{v}^2}{r}$. This force acts outwards.

The minimum speed occurs when the force acting is equal to the weight of the body as given below

$T+mg=\frac{m{v}^2}{r}$

$T_{min}=0$

$v=\sqrt{gr}$

Hence the minimum speed should be the square root of gr which keeps on rotating the body in air.