A solid sphere of radius R and made of material of bulk modulus K is completely immersed in a liquid in a cylindrical container. A massless piston of area A floats on the surface of the liquid. When a mass 5M is placed on the piston to compress the liquid, the fractional change in the radius of the sphere, $3:2$ is given by

Pressure exerted by the piston on the liquid when a mass 5M is placed on the piston, $P=5Mg/A$ . This pressure is exerted by the liquid equally in all directions. Therefore, the surface of the sphere experiences a force P per unit area. The stress on the sphere is $P=5Mg/A$ . Now, the volume of the sphere is

$V=\frac{4\pi R^3}{3}$

Due to stress, the change in the volume of the sphere is

$\Delta V=\Delta \left(\frac{4\pi R^3}{3}\right)=\frac{4\pi }{3}.3R^2\Delta R$

$=4\pi R^2\Delta R$

$\therefore volumestrain\frac{\Delta V}{V}=\frac{3\Delta R}{R}$  

By definition, bulk modulus

$K=\frac{stress}{stain}=\frac{5Mg/A}{3\Delta R/R}$

or  $\frac{\Delta R}{R}=\frac{5Mg}{3KA}$