question_answer

A uniform long tube is bent as shown. It lies in verticle plane. Two liquids of same volume but densities P and \[\delta \] fill half the tube. The angle \[\theta \] is

A)  \[\frac{p-\delta }{p+\delta }\]                

B)  \[\frac{p+\delta }{p-\delta }\]

C)  \[\sqrt{\frac{p}{\delta }}\]                     

D)  \[\sqrt{\frac{\delta }{p}}\]

Correct Answer: A

Solution :

From figure \[\delta gR\left( cos \theta  + sin \theta  \right) =PgR\,(cos\theta  - sin \theta )\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\sin \theta \left( \delta +P \right)\,\,=\,\,cos\theta \left( P-\delta  \right)\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\tan \theta =\frac{P-\delta }{P+\delta }\]