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 :
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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