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 crosssection 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
JEE MAIN 2018, Medium
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$\Delta P = \frac{{mg}}{a}$
$k = - \frac{{\frac{{mg}}{A}}}{{\frac{{4\pi {r^2}dr}}{{\frac{4}{3}\pi {r^3}}}}}$
$\frac{{dr}}{r} = - \frac{{mg}}{{3KA}}$
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