Question

A thin uniform circular tube is kept in a vertical plane. Equal volumes of two immiscible liquids whose densities are ${\rho }_1$ and ${\rho }_2$ fill half of the tube as shown.In equilibrium the radius passing through the interface makes an angle of ${30}^{\circ }$ with vertical. The ratio of densities $\left({\rho }_1/{\rho }_2\right)$ is equal to

• A. $\frac{\sqrt{3}-1}{2-\sqrt{3}}$
• B. $\frac{\sqrt{3}+1}{2+\sqrt{3}}$
• C. $\frac{\sqrt{3}-1}{\sqrt{3}+1}$
• D. $\frac{\sqrt{3}+1}{\sqrt{3}-1}$

Answer 1

The correct option is D $\frac{\sqrt{3}+1}{\sqrt{3}-1}$