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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 38

  • question_answer
    A container has two immiscible liquids of densities \[{{\rho }_{1}}\] and \[{{\rho }_{2}}(>{{\rho }_{1}})\]. A capillary tube of radius r is inserted in the liquid so that its bottom reaches up to the denser liquid. The denser liquid rises in the capillary and attains a height h from the interface of the liquids, which is equal to the column lengths of the lighter liquid. Assuming angle of contact to be zero, the surface tension of heavier liquid is

    A) \[2\pi r{{\rho }_{2}}gh\]            

    B) \[\frac{{{\rho }_{2}}rgh}{2}\]

    C) \[\frac{gh({{\rho }_{1}}-{{\rho }_{2}})r}{2}\]    

    D) \[2pr({{\rho }_{2}}-{{\rho }_{1}})\]

    Correct Answer: C

    Solution :

    [c] Angle of contact = zero R = radius of capillary = r Equating pressure at interface \[{{P}_{atm}}+\left( h\,\,{{\rho }_{1}}\,\,g \right)={{P}_{atm}}-\frac{2T}{R}+\left( h\,\,{{\rho }_{2}}\,\,g \right)\] \[T=\frac{gh\,\left( {{\rho }_{1}}-{{\rho }_{2}} \right)r}{2}\]       


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