#### 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

Let m be the mass of the stone.

Let v be the velocity of the stone at the highest point.

R is the radius of the circle.

Thus, in a vertical circle and at the highest point,

we have :

\[\frac{\text{mv}^2}{\text{R}} = \text{mg}\]

\[ \Rightarrow \text{v}^2 = \text{Rg}\]

\[ \Rightarrow \text{v} = \sqrt{\text{Rg}}\]

Is there an error in this question or solution?

Solution 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. Concept: Circular Motion.