Water rises to a height of `10cm` in a certain capillary tube. An another identical tube when dipped in mercury is depressed by `3.42 cm`.Density of mercury is `13.6 g//c c`.The angel of contact for water in contact with glass is `0^(@)` and mercury in contact with glass is `135^(@)`. The ratio of surface tension of water to that of `Hg` 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_(2)=(2xxT_(w)xxcos0^@)/(rxx1xxg)`
And for mercury
`h_(m)=(2xxT_(m)xxcos135^@)/(rxx13.6xxg)`
`:. (h_(w))/(h_(m))=(2xxT_(w)xx1)/(rxx1xxg)xx(rxx13.6xxgxxsqrt(2))/(2xxT_(m)xx1)`
`[:'cos135^@=-1//sqrt(2)]`
`implies 10/3.42=(T_(w))/(T_(m)) xx13.6xxsqrt(2)`
`:. (T_(w))/(T_(m))-10/(3.42xx13.6xx1.414)=16.5`
`:. T_(w):T_(m)=1:6.5.`