The normal density of a material 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 $P$ is applied uniformly on all sides, will be :

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

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

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

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

Correct Option: , 2

Solution:

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

$\frac{\mathrm{d} \rho}{\rho}=-\frac{\mathrm{dV}}{\mathrm{V}}$

$\mathrm{k}=-\frac{\mathrm{P}}{\frac{\mathrm{dV}}{\mathrm{V}}}$

$-\frac{\mathrm{dV}}{\mathrm{V}}=\frac{\mathrm{P}}{\mathrm{k}}$

$\frac{d \rho}{\rho}=\frac{P}{k} \Rightarrow d \rho=\frac{\rho P}{k}$

 

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