The velocity of a body revolving in a vertical circle of radius “r” at the lowest point is $\sqrt{7\mathrm{gr}}$. The ratio of maximum to minimum tensions in the string to which the body is tied is

Maximum tension will be at bottom point,

${\mathrm{T}}_{\max }=\frac{{\mathrm{m}\left({\mathrm{v}}_{\mathrm{bottom}}\right)}^2}{\mathrm{r}}+\mathrm{mg}$

${\mathrm{T}}_{\max }=\frac{\mathrm{m}\left(7\mathrm{gr}\right)}{\mathrm{r}}+\mathrm{mg}=8\mathrm{mg}$

Minimum tension will be at topmost point,

${\mathrm{T}}_{\min }=\frac{{\mathrm{m}\left({\mathrm{v}}_{\mathrm{top}}\right)}^2}{\mathrm{r}}-\mathrm{mg}$

${\mathrm{v}}_{\mathrm{top}}=\sqrt{{\left({\mathrm{v}}_{\mathrm{bottom}}\right)}^2-2\mathrm{g}\left(2\mathrm{r}\right)}=\sqrt{3\mathrm{gr}}$

${\mathrm{T}}_{\min }=\frac{\mathrm{m}\left(3\mathrm{gr}\right)}{\mathrm{r}}-\mathrm{mg}=2\mathrm{mg}$

$\Rightarrow \frac{{\mathrm{T}}_{\max }}{{\mathrm{T}}_{\min }}=\frac{8\mathrm{mg}}{2\mathrm{mg}}=\frac{4}{1}$