A solid sphere of radius


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

  1. $\frac{\mathrm{Ka}}{3 \mathrm{mg}}$

  2. $\frac{\mathrm{mg}}{3 \mathrm{Ka}}$

  3. $\frac{\mathrm{mg}}{\mathrm{Ka}}$

  4. $\frac{\mathrm{Ka}}{\mathrm{mg}}$

Correct Option: , 2


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