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, ($\frac{\text{d}r}{\text{}r}$) is

Answer:

Explanation:

$\therefore$   Bulk modulus.

 K= $\frac{Volumetric stress }{Volumetric strain} =\frac{\triangle p}{\frac{\triangle v}{v}}$

$\Rightarrow K=\frac{mg}{a(\frac{3\triangle r}{r})} [\therefore V=\frac{4}{3}\pi r^{3}, so \frac{\triangle V}{V}=\frac{3\triangle r}{r} ]$

$\Rightarrow $             $\frac{\triangle r}{r}=\frac{mg}{3aK}$