Question

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $d_1$ and $d_2$ are filled in the tube. Each liquid subtends ${90}^o$ angle at centre. Radius joining their Interface makes an angle an angle $\alpha$ with vertical. Ratio $d_1/d_2$ is

• A. $\frac{1+\tan \alpha }{1-\tan \alpha }$
• B. $\frac{1+\sin \alpha }{1-\cos \alpha }$
• C. $\frac{1+\sin \alpha }{1-\sin \alpha }$
• D. $\frac{1+\cos \alpha }{1-\cos \alpha }$

Answer 1

The correct option is A $\frac{1+\tan \alpha }{1-\tan \alpha }$

The concept is that:

The pressure at the interface must be same from both the sides to be equilibrium

$d_{1}gR(\cos \alpha -\sin \alpha )=d_{2}gR(\cos \alpha +\sin \alpha )$

therefore:

$\frac{d_1}{d_2}=\frac{1+\tan \alpha }{1-\tan \alpha }$