Water rises to a height of `10 cm` in a capillary tube and mercury falls to a depth of `3.42 cm` in the same capillary tube. If the density of mercury is `13.6 g//c.c.` and the angles of contact for mercury and for water are `135^@` and `0^@`, respectively, the ratio of surface tension for water and mercury is

Options

A. `1:2`
B. `1:13.6`
C. `1:3.42`
D. `1: 6.58`

Answer

D

Explanation

`T_("water")= (rh_(w)rho_(w)g)/(2 cos theta_(1)) xx (2 cos theta_(2))/(rh_(m)rho_(m)g)`
` = (h_(w)rho_(w))/(h_(m)rho_(m)) xx (cos theta_(2))/(cos theta_(1))`
` (10xx1 xx cos135^(@))/((-3.42)xx1.36 xxcos0^(@))`
` (10 xx (-0.7071))/((-3.42)xx1.36) =(7.071)/(3.42 xx13.6)`