Water rises to a height of 10 cm in capillary tube and mercury falls to a depth of 3.112 cm in the same capillary tube. If the density of mercury is 13.6 and the angle of contact for mercury is `135^(@)`, the ratio of surface tension of water and mercury is

Explanation

`h=(2T cos theta)/(rpg)`
For water,
`10cm=(2xxT_(W)xxcos 0^(@))/(rxx1xxg)" ….(1)"`
For mercury,
`-3.42cm=(2xxTMxxcos 135^(@))/(rxx13.6xxg)" ….(2)"`
Dividing `"Eq"^(n)(1) " by "(2)`
`(10)/(-3.42)=(2xxT_(w)xx1xxrxx13.6xxg)/(rxx1xxgxx2xxT_(M)xx(-1)/(sqrt2))`
`rArr (10)/(3.42)=sqrt2xx13.6xx(T_(W))/(T_(M))`
`rArr(10)/(3.42xx1.41xx13.6)=(T_(W))/(T_(M))`
`rArr(1)/(6.5)=(T_(W))/(T_(M))`