question_answer

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 \[\alpha \] with vertical. Ratio \[\frac{{{d}_{1}}}{{{d}_{2}}}\]is   JEE Main  Solved  Paper-2014

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) \[\frac{1+\cos \alpha }{1-\cos \alpha }\]

Correct Answer: A

Solution :

Pressure at 0 level is same from both sides. \[{{d}_{1}}(1-sin\alpha )={{d}_{1}}(1-cos\alpha )+{{d}_{2}}[cos\alpha +sin\alpha ]\] \[\Rightarrow \]\[\frac{{{d}_{1}}}{{{d}_{2}}}=\frac{\sin \alpha +\cos \alpha }{\cos \alpha -\sin \alpha }\]