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:

• A

  $\frac{mg}{Ka}$
• B

  $\frac{Ka}{mg}$
• C

  $\frac{Ka}{3mg}$
• Correct answer
  D

  $\frac{mg}{3Ka}$

Hence, the correct answer is option: 'D'.