Question

The bulk modulus of a spherical object is $B$. If it is subjected to uniform pressure $P$, the fractional decrease in radius is

• A. $\frac{P}{B}$
• B. $\frac{B}{3P}$
• C. $\frac{3P}{B}$
• D. $\frac{P}{3B}$

Answer 1

The correct option is D $\frac{P}{3B}$

$|B|=\left|\frac{-\Delta P}{\Delta V/V}\right|$

$B=\frac{p}{\Delta v/v}$

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

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

$\frac{\Delta V}{V}=3\frac{\Delta r}{r}$

$\begin{array}{cc}\frac{3\Delta r}{r}& =\frac{p}{B}\\ \frac{\Delta r}{r}& =\frac{p}{3B}\end{array}$