Question

A small solid sphere of radius R made of a material of bulk modulus B is surrounded by an incompressible liquid in a cylindrical container. A massless piston of area A floats on the surfaces of the liquid. Find the magnitude of fractional change in the radius of the sphere $\left(\frac{dR}{R}\right)$ when a mass M is placed slowly on the piston to compress the liquid.

• A. $\frac{Mg}{3AB}$
• B. $\frac{Mg}{AB}$
• C. $\frac{3Mg}{AB}$
• D. None of these

Answer 1

The correct option is B

$\frac{Mg}{AB}$

$V=\frac{4}{3}\pi R^3\frac{dR}{R}=\frac{1}{3}\frac{dV}{V}B=-V\frac{dP}{dV}\left|\frac{dV}{V}\right|=\frac{dP}{B}=\frac{Mg}{AB}$