Question

A solid sphere of radius R made of material of bulk modulus k is surrounded by a liquid in a cylindrical container. A maseless piston of area. A flats on the surface of the liquid. When a mass m is placed on the position to compress the liquid, fractional change in the radius of the sphere $\frac{△R}{R}$ is :

• A. $\frac{mg}{3AR}$
• B. $\frac{mg}{A}$
• C. $\frac{mg}{3AK}$
• D. $\frac{mg}{AK}$

Answer 1

Answer: (C)

$\frac{mg}{3AK}$

For a spherical body,

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

$\therefore \frac{\Delta R}{R}=\frac{1}{3}\frac{\Delta V}{V}$

Since bulk modulus, $K=-V\frac{\Delta P}{\Delta V}$

$\frac{\Delta V}{V}=\frac{\Delta P}{K}=\frac{mg}{AK}$

$\frac{\Delta R}{R}=\frac{mg}{3AK}$