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Manipal Medical Manipal Medical Solved Paper-2014

  • 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 flats on the surface of the liquid. When a mass m is placed on the piston to compress the liquid, fractional change in the radius of the sphere \[\frac{\Delta R}{R}\] is

    A) \[\frac{mg}{3AR}\]                            

    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 \[\frac{\Delta V}{V}=\frac{\Delta p}{p}=\frac{mg}{AK}\Rightarrow \frac{\Delta R}{R}=\frac{1}{3}\frac{mg}{AK}\]


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