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A solid sphere of radius r made of a soft 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, covering entire cross section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ r dr , is -

1. mg Ka
2. mg Ka 3
3. Ka mg 3
4. Ka mg Students may find similar question in CP exercise sheet : [ JEE Main, Chapter : Properties of Matter (Elasticity) ]

Correct answer: Ka mg 3

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