The ratio of surface tensions of mercury and water is given to be 7.5 while the ratio of their densities is 13.6. Their contact angles with glass are 135°C and 0°C respectively. It is observed that mercury gets depressed by an amount h in a capillary tube of radius $r_{1}$ while water rises by the same amount h is a capillary tube of radius $r_{2}$ . Then $\frac{r_{1}}{r_{2}}$ is

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$\frac{3}{5}$

$\frac{2}{3}$

$\frac{2}{5}$

$\frac{4}{5}$

answer is C.

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Detailed Solution

$h = \frac{2 Tcos θ}{rρg}$
$\frac{r_{Hg}}{r_{w}} = \frac{T_{Hg}}{T_{w}} \cdot \frac{\cos θ_{Hg}}{\cos θ_{w}} \cdot \frac{ρ_{w}}{ρ_{Hg}} = (7.5) (\frac{1}{\sqrt{2}}) (\frac{1}{13 .6}) = 0 .4 = \frac{2}{5}$

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