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

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

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

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

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

Administrator

Leave a comment

Please enter comment.
Please enter your name.