Two capillary tubes of the same diameter are kept vertically in two liquids whose densities are in the ratio `4 :3` What is the ratio of the heights `(h_(1)/(h_(2)))` in the two capillary tubes if their surface tension are int the ratio of `6 :5` [ Assume that their angles of contact are equal ]

Options

A. `10/9`
B. `9/10`
C. `5/10`
D. `10/7`

Answer

B

Explanation

Given : ` (T_(1))/(T_(2)) =6/5 and (rho_(1))/(rho_(2)) =4/3`
For rise of a liquid in a capillary `rhrhog= 2T cos theta`
In this case `cos theta_(1) = cos theta_(2) and r_(1) =r_(2)`
` :. (h_(1)rho_(1))/(h_(2)rho_(2)) =(T_(1))/(T_(2))`
` :. (h_(1))/(h_(2)) -(T_(1)rho_(g))/(T_(2)rho_(1)) = 6/5 xx3/4 = 9/10`