# The normal density of a material is $ho$ and its bulk modulus of elasticity is

Question:

The normal density of a material is $\rho$ and its bulk modulus of elasticity is

$\mathrm{K}$. The magnitude of increase in density of material, when a pressure $\mathrm{P}$ is applied uniformly on all sides, will be :

1. $\frac{\rho K}{P}$

2. $\frac{\mathrm{K}}{\rho \mathrm{P}}$

3. $\frac{\mathrm{PK}}{\rho}$

4. $\frac{\rho P}{K}$

Correct Option: , 4

Solution:

(4)

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

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

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

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

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

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