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. ` (r rho _ 2 gh )/(2) `
B. ` 2 rho_1 r rho _2 g h `
C. ` (r )/(2) (rho_2 - rho _ 1 )gh `
D. `2pi r ( rho_2 - rho _1 ) gh `

Answer

C

Explanation

At interface ` P _ 0 + rho_1 gh = P _ 0 - (2T )/(r ) + rho _ 2 gh `