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WB JEE Medical WB JEE Medical Solved Paper-2010

  • question_answer
    A uniform long tube is bent into a circle of radius R und it lies in vertical plane. Two liquids of same volume but densities \[\rho \]and \[\delta \] fill half the tube. The angle \[\theta \] is

    A)  \[{{\tan }^{-1}}\left( \frac{\rho -\delta }{\rho +\delta } \right)\]

    B)  \[{{\tan }^{-1}}\left( \frac{\rho }{\delta } \right)\]

    C)  \[{{\tan }^{-1}}\left( \frac{\delta }{\rho } \right)\]                           

    D)  \[{{\tan }^{-1}}\left( \frac{\rho +\delta }{\rho -\delta } \right)\]

    Correct Answer: A

    Solution :

                     From the figure, we have \[\delta gR(cos\theta +sin\theta )=\rho gR(cos\theta -sin\theta )\] \[\Rightarrow \]  \[\delta \cos \theta +\delta \sin \theta =\rho \cos \theta -\rho \sin \theta \] \[\Rightarrow \]   \[\sin \theta (\delta +\rho )=cos\theta (\rho -\delta )\] \[\Rightarrow \]               \[\tan \theta =\frac{\rho -\delta }{\rho +\delta }\]


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