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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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