A stone attached to one end of a string is whirled in a vertical circle. The tension in the string is maximum when

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

where, $\theta$ is angle made by the string with downward vertical.

$$\begin{gathered} \mathrm{For} {\mathrm{T}}_{\max }: \mathrm{\theta }=0^{\mathrm{o}} \\ \Rightarrow {\mathrm{T}}_{\max }=\frac{{\mathrm{mv}}^2}{\mathrm{r}}+\mathrm{mg} \end{gathered}$$

Here, the stone is at the lowest position in the vertical circle where velocity is also maximum.