A solid sphere of radius r made of a soft material of bulk modulus K… | JEE Main 2018

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Bulk Modulus & Compressibility

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, $\left(\frac{dr}{r}\right)$ is:

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Answer: (d)

Extra pressure in the liquid (Pascal's law): $P = \frac{mg}{a}$ , acting on the sphere from all sides.
$\frac{\Delta V}{V} = \frac{P}{K} = \frac{mg}{Ka}$
$\frac{\Delta V}{V} = 3\frac{dr}{r} \Rightarrow \frac{dr}{r} = \frac{mg}{3Ka}$
So the answer is (d).

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