The ratio of surface tensions of mercury and water is given to be...

$| {h}_{Hg} | = | {h}_{water} |$

$\dfrac{2{S}_{1}cos{\theta}_{1}}{{ρ}_{1}{r}_{1}g} = \dfrac{2{S}_{2}cos{\theta}_{2}}{{ρ}_{2}{r}_{2}g}$

Therefore, the ratio of the radii of the respective tubes is,

$\dfrac{{r}_{1}}{{r}_{2}} = \dfrac{{ρ}_{2}}{{ρ}_{1}} \times \dfrac{{S}_{1}cos{\theta}_{1}}{{S}_{2}cos{\theta}_{2}}$

$\dfrac{{r}_{1}}{{r}_{2}} = \dfrac{1}{13.6} \times 7.5 \times \dfrac{1}{\sqrt{2}}$

$\dfrac{{r}_{1}}{{r}_{2}} \approx \dfrac{2}{5}$