Question

If B is the bulk modulus of a metal and a pressure p is applied uniform on all sides of the metal with density D, then the fractional increase in density is given by

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

Answer 1

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

The bulk modulus, $B=\frac{P}{\Delta V/V}$

$\frac{\Delta V}{V}=\frac{P}{B}$. . . . . . .(1)

We know that, $D\propto \frac{1}{V}$

$\frac{D^{\prime }}{D}=\frac{V}{V-\Delta V}=V(V-\Delta V{)}^{-1}$

$\frac{D^{\prime }}{D}=1+\frac{\Delta V}{V}$

$\frac{D^{\prime }-D}{D}=\frac{\Delta V}{V}$

$\frac{D^{\prime }-D}{D}=\frac{P}{B}$

The correct option is B.