Question

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 the entire crosssection of the cyindrical 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. $\frac{2mg}{3Ka}$
• B. $\frac{mg}{3Ka}$
• C. $\frac{Ka}{mg}$
• D. $\frac{Ka}{3mg}$

Answer 1

The correct option is B $\frac{mg}{3Ka}$

$\Delta P=\frac{mg}{a}K=\frac{\left(\frac{mg}{a}\right)}{\left(}\frac{\Delta V}{V}=-\frac{mg}{Ka}Weknow,\frac{\Delta V}{V}=3\frac{\Delta r}{r}\frac{\Delta r}{r}=\frac{-mg}{3KA}$