Question

A material has normal density $\rho$ and bulk modulus $K$. The increase in the density of the material when it is subjected to an external pressure $P$ from all sides is

• A. $P/\rho K$
• B. $K/\rho P$
• C. $P\rho /K$
• D. $K\rho /P$

Answer 1

The correct option is C $P\rho /K$

We know that $K=-V\frac{dP}{dV}$
Also as mass remains constant we have $\frac{dV}{V}=\frac{d\rho }{\rho }$
Thus we get
$K=-\rho \frac{dP}{d\rho }$
Here $dP=P$
Thus we get
$d\rho =-\frac{\rho P}{K}$