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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 8

  • question_answer
    If the weight of a body in vacuum is W, and \[{{W}_{1}}\]and \[{{W}_{2}}\]are weights when it is fully immersed in liquids of specific gravities \[{{\rho }_{1}}\] and \[{{\rho }_{2}}\] respectively, then the relation among W, \[{{W}_{1}}\] and \[{{W}_{2}}\] is

    A)  \[W=\frac{{{W}_{1}}{{\rho }_{2}}+{{W}_{2}}{{\rho }_{1}}}{{{W}_{1}}+{{W}_{2}}}\]     

    B)  \[W=\frac{{{W}_{1}}{{\rho }_{2}}-{{W}_{2}}{{\rho }_{1}}}{{{\rho }_{2}}-{{\rho }_{1}}}\]

    C) \[W=\frac{{{W}_{1}}{{\rho }_{2}}+{{W}_{2}}{{\rho }_{1}}}{{{\rho }_{1}}+{{\rho }_{2}}}\]           

    D) \[W=\frac{{{W}_{1}}{{\rho }_{2}}-{{W}_{2}}{{\rho }_{1}}}{{{\rho }_{1}}-{{\rho }_{2}}}\]

    Correct Answer: B

    Solution :

    [b] Loss in weight of liquid of density \[{{\rho }_{1}}\] is \[(W-{{W}_{1}})kg.\] Volume of liquid displaced, \[V=\frac{W-{{W}_{1}}}{{{\rho }_{1}}}\] Similarly, for 2nd liquid volume displaced    \[V=\frac{W-{{W}_{1}}}{{{\rho }_{2}}}\] \[\therefore \,\,\,\,\,\,\frac{W-{{W}_{1}}}{{{\rho }_{1}}}=\frac{W-{{W}_{2}}}{{{\rho }_{2}}}\]


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