Question

The normal density of a material is $\rho$ and its bulk modulus of elasticity is $K$. The magnitude of increase in density of material, when a pressure $P$ is applied uniformly on all sides, will be:

• A. $\frac{\rho K}{P}$
• B. $\frac{K}{\rho P}$
• C. $\frac{PK}{\rho }$
• D. $\frac{\rho P}{K}$

Answer 1

The correct option is D $\frac{\rho P}{K}$

Bulk modulus $K=\frac{-P}{\frac{\Delta V}{V}}$

We know, $\rho =\frac{M}{V}$

So, $\frac{-\Delta \rho }{\rho }=\frac{\Delta V}{V}$

$K=$ $\frac{-P}{(-\frac{\Delta \rho }{\rho })}=\frac{\rho P}{\Delta \rho }$

$\Delta \rho =\frac{\rho P}{K}$