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.

Solution

The force acting on the body moving in a circle is centrifugal which is given as $${F_c} = \dfrac{{m{v^2}}}{r}$$. This force acts outwards. The minimum speed occurs when the force acting is equal to the weight of the body as given below $$T + mg = \dfrac{{m{v^2}}}{r}$$ $${T_{\min }} = 0$$ $$v=\sqrt {gr}$$Hence the minimum speed should be the square root of gr which keeps on rotating the body in air.  Physics

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