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MGIMS WARDHA MGIMS WARDHA Solved Paper-2015

  • question_answer
    A solid sphere of radius r made of a material of bulk modulus K is surrounded by a liquid in cylindrical container. The massless piston of area A floats on the surface of the liquid. If a mass m is placed on a piston to compress the liquid, then the fractional change in the radius of the sphere will be

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

    B)  \[\frac{2mg}{AK}\]

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

    D)  \[\frac{mg}{3AK}\]

    Correct Answer: D

    Solution :

                     When mass m is placed on the piston, the excess pressure will be\[p=\frac{mg}{A}\]. This pressure acts equally from all the directions on the solid sphere. So, the radius of sphere decreases which in turn decreases the volume of sphere. \[\because \]     \[V=\frac{4}{3}\pi {{r}^{3}}\] So            \[\frac{\Delta V}{V}=3\frac{\Delta r}{r}\] Now, bulk modulus \[K=\frac{p}{\frac{\Delta V}{V}}\] \[\Rightarrow \]               \[\frac{\Delta V}{V}=\frac{p}{K}=\frac{mg}{A}\times \frac{1}{K}\] \[\Rightarrow \]               \[3\frac{\Delta r}{r}=\frac{mg}{AK}\] \[\therefore \]  \[\frac{\Delta r}{r}=\frac{mg}{3AK}\]


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