Q. A solid sphere of radius R made up of a 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. When a mass M is placed on the piston to compress the liquid, the fractional change in the radius of the sphere is
A) $\frac{Mg}{AK}$
B) $\frac{Mg}{3AK}$
C) $\frac{3Mg}{AK}$
D) $\frac{Mg}{2AK}$
Explanation
(b) Change in pressure due to placing of mass on piston is,
$\mathrm{\Delta}p = \frac{Mg}{A}$
From Bulk modulus definition
$K = \frac{- dp}{\frac{dV}{V}}$
⟹ $\left| \frac{dV}{V} \right| = \frac{\mathrm{\Delta}p}{K} = \frac{Mg}{AK}$
$From\ \ V = \frac{4}{3}\pi r^{3}$
$\frac{dV}{V} = \frac{3dR}{R}$
$\Longrightarrow \ \frac{dR}{R} = \frac{1}{3}\frac{dV}{V}$
$= \frac{Mg}{3AK}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.