Question

The bulk modulus of a spherical object is B. If it is subjected to uniform pressure P, the fractional decrease in its 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 $\frac{P}{3B}$

As Bulk modulus is given as, $B=\frac{△P}{-\frac{△V}{V}}$

$B=\frac{V△P}{△V}$
Volume $\left(V\right)$ of sphere $=\frac{4}{3}\pi r^3$
$\Delta V=4\pi r^2\Delta r$
then, $\frac{V}{△V}=\frac{r}{3△r}$

$B=\frac{r\Delta P}{3\Delta r}$

$\Rightarrow -\frac{△r}{r}=\frac{P}{3B}(△P=P)$