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JEE Main & Advanced Sample Paper JEE Main Sample Paper-44

  • question_answer
    A solid sphere of radius R, made up of a material of bulk modulus K is surrounded by a liquid in a cylindrical container. A mass less 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 is

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

    B)  \[\frac{Mg}{3AK}\]

    C)  \[\frac{3Mg}{AK}\]               

    D)  \[\frac{Mg}{2AK}\]

    Correct Answer: B

    Solution :

     Change in pressure due to placing of mass on piston is, \[\Delta p=\frac{Mg}{A}\]             From bulk modulus, definition, \[K=\frac{-dp}{dV/V}\] \[\Rightarrow \]            \[\left| \frac{dV}{V} \right|=\frac{\Delta p}{K}=\frac{Mg}{AK}\] From    \[\frac{dV}{V}=3\frac{dR}{R}\]      \[\left[ \because \,\,V=\frac{4}{3}\,\pi {{R}^{3}} \right]\] \[\Rightarrow \]            \[\frac{dR}{R}=\frac{1}{3}\,\frac{dV}{V}=\frac{Mg}{3AK}\]


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