Discussion Forum

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 $\frac{dr}{r}$ is

Answer:

Explanation:

Bulk modulus.

$K= \frac{Volumetric stress}{Volumetric strain}$

$=\frac{\frac{\triangle p}{V}}{V}$

$K=\frac{mg}{a(\frac{3\triangle r}{r})}$

$v=\frac{4}{3}\pi^{3}$

$\frac{\triangle V}{V}=\frac{3\triangle r}{r}$

$\frac{\triangle r}{r}=\frac{mg}{3Ka}$