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)/(r rhog)`
For water `h_W=(2xxT_Wxxcos)^@)/(rxx1xxg)`
And for mercury
`h_m=-(2xxT_mxxcos135^@)/(rxx13.6xxg)` .(ii)
`(h_w)/(h_m)=(2xxT_wxx1)/(rxx1xxg)xx(rxx13.6xxgxxsqrt2)/(2xxT_mxx1)`
`[becausecostheta135^@=(-1)/(sqrt2)]`
`implies(10)/(3.42)=(T_w)/(T_m)xx13.6xxsqrt2`
`(T_w)/(T_m)=(10)/(3.42xx13.6xx1.414)=(1)/(6.5)`
Therefore, `T_w:T_m=1:6.5`