Question

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 ${\rho }_1({\rho }_1<{\rho }_2)$ 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

• A. $r{\rho }_{2}gh$
• B. $2\pi r{\rho }_{2}gh$
• C. $\frac{r}{2}({\rho }_2-{\rho }_1)gh$
• D. $2\pi r({\rho }_2-{\rho }_1)gh$

Answer 1

The correct option is C $\frac{r}{2}({\rho }_2-{\rho }_1)gh$

In the given figure:-

$\begin{array}{c}{\rho }_{\circ }+{\rho }_{1}gh-{\rho }_{2}gh+\frac{2s}{r}={\rho }_{\circ }\\ Hence,\\ S=\frac{r\left({\rho }_2-{\rho }_1\right)gh}{2}\end{array}$

$\therefore$ option $C$ is correct answer.