A container is partially filled with a liquid of density `rho_2` A capillary tube of radius r is vertically inserted in this liquid. Now another liquid of density `rho_1(rho_1ltrho_2)` is slowly poured in the container to a height h as shown. There is only denser liquid in the capillary tube. The rise of denser liquid in the capillary tube is also `h`. Assuming zero contact angle, the surface tension of heavier liquid is

Options

A. `(1 - x_2)/(x_1 - x_2)`
B. `(1 - x_1)/(x_1 + x_2)`
C. `(x_1 - x_2)/(x_1 + x_2)`
D. `x_2/x_1 - 1`

Answer

A

Explanation

Let V be volume of the block and p density of the block. For the first case,

equating (i) and (ii) , we get
`x_1rho_1 = x_2rho_1 + (1- x_2)rho_2`
`(x_1 - x_2) rho_1 = (1 - x_2) rho_2`
`rho_1/rho_2 = (1-x_2)/(x_1 - x_2)`