Question

A solid sphere of radius $r$ made of a material of bulk modulus $B$ is surrounded by a liquid in a liquid in a cylindrical container. A mass less piston of area a floats on the surface of the liquid. When a mass $m$ is placed on the piston compress the liquid, the fraction change in the radius of the sphere $\left(dr/r\right)$ is :

• A. $Ba/mg$
• B. $Ba/3mg$
• C. $mg/3Ba$
• D. $mg/Ba$

Answer 1

The correct option is C $mg/3Ba$

$\Delta P=\frac{mg}{a}$

$\frac{\Delta V}{V}=\frac{\Delta p}{B}$

$\begin{array}{cc}v=\frac{4}{3}\pi g^3& \\ \frac{\Delta v}{v}=\frac{3\Delta n}{r}& \\ \frac{3\Delta g}{r}=\frac{mg}{a\beta }& \\ \frac{\Delta r}{r}=\frac{mg}{3a\beta }& \end{array}$