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

Options

A. `1:0.15`
B. `1:3`
C. `1:6`
D. `1.5:1`

Answer

C

Explanation

`h = (2 sigma cos theta)/(r rho g ) implies sigma prop (h rho )/( cos theta) implies (sigma _(w))/( sigma _(m)) = (h _(w) rho _(w))/( cos theta _(w)) xx (cos theta _(m))/( h _(m) rho _(m))`
`= (10 xx 1)/( cos 0^(@))xx (cos 135 ^(@))/( -3.1 xx 13.6 ) = (10 xx (-0. 707))/( -3.1 xx 13.6)~~ 1/6`