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VMMC VMMC Medical Solved Paper-2011

  • question_answer
    A solid sphere of radius R made of material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area A floats on the surface of the liquid. When amass m is placed on the piston         to compress the liquid, fractional change in the radius of the sphere\[\frac{\Delta R}{R}\] is

    A)  \[\frac{mg}{3\,AR}\]     

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

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

    D)        \[\frac{mg}{AK}\]

    Correct Answer: C

    Solution :

                            For a spherical body \[V=\frac{4}{3}\pi {{R}^{3}}\] Differentiating and solving, we get \[\frac{\Delta R}{R}=\frac{1}{3}\frac{\Delta V}{V}\] We know that \[K=-\,V\frac{\Delta p}{\Delta V}\] Negative signs shows that when pressure is increased volume will decrease. i.e.,        \[\frac{\Delta V}{V}=\frac{\Delta p}{K}=\frac{mg}{AK}\]                \[\left[ \because \Delta p=\frac{mg}{A} \right]\] Hence, \[\frac{\Delta R}{R}=\frac{1}{3}\frac{mg}{AK}\]


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