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  • A material has normal density ρ and bulk modulus B. The increase in density of the material when it is subjected to an external additional p

A material has normal density ρ and bulk modulus B. The increase in density of the material when it is subjected to an external additional pressure P from all sides is

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\\ B (\text{Bulk modulus}) =\frac{-P}{\frac{\Delta V}{V}}---$ (1) \\ Also, $\rho=\frac{m}{V}$ \\ \\ $\Rightarrow \rho=m V^{-1}$ \\ \\ $\Rightarrow \frac{\Delta \rho}{\rho}=\frac{\Delta m}{m}-\frac{\Delta V}{V}$ \\ \\ As mass is constant, $\Delta m=0$ \\ \\ So, $\frac{\Delta \rho}{\rho}=\frac{-\Delta V}{V}$ \\ From (i) and (ii), we get \\ \\

B=\frac{-P}{\frac{-\Delta \rho}{\rho}}$ \\ \\ \\ $\Rightarrow \frac{\Delta \rho}{\rho}=\frac{P}{B}$ \\ \\ $\Rightarrow \Delta \rho=\frac{P}{B} \rho$ \\ \\

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