$A$ 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 the entire cross-section of the 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:

• A
  $\frac{Ka}{3mg}$
• B
  $\frac{mg}{3Ka}$
• C
  $\frac{mg}{Ka}$
• D
  $\frac{Ka}{mg}$