Question

A solid sphere of radius $R$ made of 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 liquid. When a mass $m$ is placed on the piston to compress the liquid, the fractional change in the radius of the sphere $\delta R/R$ is :

• A. $mg/AK$
• B. $mg/3AK$
• C. $mg/A$
• D. $mg/3AR$

Answer 1

The correct option is B $mg/3AK$

$\frac{\Delta V}{V}=\frac{P}{K}$
Now, $\frac{\Delta V}{V}=\frac{3\delta R}{R}$
and $P=\frac{mg}{A}$
So, $\frac{3\delta R}{R}=\frac{mg}{AK}$
$\therefore \frac{\delta R}{R}=\frac{mg}{3AK}$