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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2011

  • question_answer
        A solid sphere of radius fi made up of a material of bulk modulus K is surrounded by a liquid in cylindrical container. A massless 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

    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       \[V=\frac{4}{3}\pi {{r}^{3}}\]                 \[\frac{dV}{V}=\frac{3dR}{R}\] \[\Rightarrow \]               \[\frac{dR}{R}=\frac{1}{3}\frac{dV}{V}=\frac{Mg}{3AK}\]


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