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 $\alpha$ with vertical. Ratio $\frac{d_1}{d_2}$ is?

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

Answer 1

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

$P_A=P_B$

$P_0+d_{1g}R(\cos \alpha -\sin \alpha )=P_0+d_{2}R(\cos \alpha +\sin \alpha )$

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