Question

The density of a metal at normal pressure is $\rho$. It's density when it is subjected to an excess pressure p is $\rho$'. If B is the bulk modulus of the metal, the ratio $\rho$'/$\rho$ is :

• A. $\frac{1}{1-p/B}$
• B. $1+\frac{P}{B}$
• C. $\frac{1}{1-B/p}$
• D. $1+B/p$

Answer 1

The correct option is A $\frac{1}{1-p/B}$

$B=-V\frac{dP}{dV}$

Thus, $\Delta V=-\frac{pV}{B}$ or $V^{\prime }-V=-\frac{pV}{B}$

Or, $V^{\prime }=V(1-\frac{p}{B})$

Now, ${\rho }^{\prime }=\frac{m}{V^{\prime }}=\frac{m}{V(1-\frac{p}{B})}=\frac{\rho }{(1-\frac{p}{B})}$