A ball of mass $$0.25\,kg$$  attached to the end of a string of length $$1.96\,m$$  is moving in a horizontal circle. The string will break if the tension is more than $$25\,N.$$  What is the maximum speed with which the ball can be moved ?

Solution :
For a ball to move in horizontal circle, the ball should satisfy the condition
Tension in the string = Centripetal force
$$ \Rightarrow {T_{\max }} = \frac{{Mv_{\max }^2}}{R}$$
$$ \Rightarrow {v_{\max }} = \sqrt {\frac{{{T_{\max }} \cdot R}}{R}} \,......\left( {\text{i}} \right)$$
Making substitution, we obtain $${v_{\max }} = \sqrt {\frac{{25 \times 1.96}}{{0.25}}} = \sqrt {196} = 14\,m/s$$
NOTE
In a vertical circle, the tension at the highest point is zero and at lowest point is maximum.