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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 33

  • question_answer
    A solid sphere of radius R made of a material of Bulk modulus K is surrounded by a liquid in a cylindrical container. A light piston of area. A floats on the surface of the liquid. When a mass m is placed on the piston to compress the liquid, the fractional change in the radius of the sphere will be

    A) \[\frac{mg}{AK}\]                                 

    B) \[\frac{3mg}{AK}\]              

    C) \[\frac{mg}{3AK}\]            

    D)        \[\frac{mg}{2AK}\]

    Correct Answer: C

    Solution :

    [c] By definition. Bulk's modulus \[K=-\frac{dP}{\left( \frac{dV}{V} \right)}=-\frac{mg/A}{dV/V}\] \[V=\frac{4}{3}\pi {{R}^{3}}\Rightarrow \frac{dV}{V}=3\frac{dR}{R},\,\,\,K=\frac{mg}{3A\left( \frac{dR}{R} \right)}\] \[\Rightarrow \,\,\,\frac{dR}{R}=-\frac{mg}{3AK}\]  


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