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. `1:0.15`
B. `1:3`
C. `1:6.5`
D. `1.5:1`

Answer

C

Explanation

Height `h=(2Tcostheta)/(rrhog)`
For water, `h_(w)=(2xxT_(w)xxcos0^(@))/(rxx1xxg)`
And, for mercury `h_(m)=(2xxT_(m)xxcos135^(@))/(rxx13.6xxg)`
`because(h_(w))/(h_(m))=(2xxT_(w)xx1)/(rxx1xxg)xx(rxx13.6xxgxxsqrt(2))/(2xxT_(m)xx1)`
`[becausecos135^(@)=(-1)/(sqrt(2))]implies(10)/(3.42)=(T_(w))/(T_(m))xx13.6xxsqrt(2)`
`because(T_(w))/(T_(m))=(10)/(3.42xx13.6xx1.414)=(1)/(6.5)`
`becauseT_(w):T_(m)=1:6:5`