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. `2 pi r rho_(2) gh`
B. `(rho_(2) rgh)/(2)`
C. `(r )/(2) (rho_(2)-rho_(1))gh`
D. `2 pi r (rho_(2)-rho_(1)) gh`

Answer

C

Explanation

Let us write pressure equation in path ABCDE.

`p_(0)-(2T)/(r )+rho_(2)g (h+h')-rho_(2)gh'-rho_(1)gh=p_(0)`
`therefore T=(r )/(2) (rho_(2)-rho_(1)) gh`