A body is moving in a vertical circle of radius ‘r’ by a string. If the ratio of maximum to minimumspeed is $\sqrt{3}:1$ , the ratio of maximum to minimum tensions in the string is

${\text{v}}_{\text{max}}=\sqrt{3}{\text{v}}_{\text{min}}$

${\text{v}}^{\text{2}}={\text{v}}^{\text{2}}-2\text{g}l\left(1-\cos \theta \right)$

${\text{v}}_{\text{min}}^{\text{2}}={\left(\sqrt{3}{\text{v}}_{\text{min}}\right)}^2-2\text{g}l\left(1-\cos \theta \right)$

${\text{v}}_{\text{m}}^{\text{2}}=\sqrt{\text{3}}{\text{v}}_{\text{m}}^{\text{2}}-2\text{g}l\left(1-\cos \theta \right)$

$\theta =180°$

$2{\text{v}}_{\text{m}}^{\text{2}}=2\text{g}l\left(2\right)$

${\text{v}}_{\text{m}}^{\text{2}}=2\text{g}l$

$\frac{{\text{v}}_{\text{m}}^{\text{2}}}{2\text{g}}=l$

${\text{T}}_{\text{max}}=\frac{{\text{mv}}^{\text{2}}}{\text{L}}+\text{mg}\cos \theta$

$=\frac{\text{m}{\left(\sqrt{3}{\text{v}}_{\text{m}}\right)}^2}{\frac{{\text{v}}_{\text{m}}^{\text{2}}}{2\text{g}}}+\text{mg}$

${\text{T}}_{\text{max}}=7\text{mg}$

${\text{T}}_{\text{min}}=\frac{{\text{mv}}_{\text{m}}^{\text{2}}}{\frac{{\text{v}}_{\text{m}}^{\text{2}}}{2\text{g}}}-\text{mg}$

${\text{T}}_{\text{min}}=2\text{gm}-\text{mg}$

${\text{T}}_{\text{max}}:{\text{T}}_{\text{min}}=7:1$