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 :
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, $\rho=\frac{M}{V}$
$\mathrm{So}, \quad \frac{-\Delta \rho}{\rho}=\frac{\Delta \mathrm{V}}{\mathrm{V}}$
$\mathrm{K}=\frac{-\Delta \mathrm{P}}{\left(-\frac{\Delta \rho}{\rho}\right)}=\frac{\rho \Delta \mathrm{P}}{\Delta \rho}$
$\Delta \rho=\frac{\rho \Delta \mathrm{P}}{\mathrm{K}}$
$\Delta \rho=\frac{\rho \mathrm{P}}{\mathrm{K}}$