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 $90^\circ$ angle at centre. Radius joining their interface makes an angle α 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

Answer: (C)

Equating pressure at A

$(R \cos \alpha+R \sin \alpha) d_{2} g=(R \cos \alpha-R \sin \alpha) d_{1} g $
$\Rightarrow \frac{d_{1}}{d_{2}}=\frac{\cos \,\alpha+\sin \,\alpha}{\cos\, \alpha-\sin \,\alpha}=\frac{1+\tan \alpha}{1-\tan\, \alpha}$