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  • The normal density of a material is and its bulk modulus of elasticity is K. The magnitude of increase in density of material, when a pressure P is applied uniformly on all s

The normal density of a material is \rho and its bulk modulus of elasticity is K. The magnitude of increase in density of material, when a pressure P is applied uniformly on all sides, will be :
 
Option: 1 \frac{K}{\rho P}
Option: 2 \frac{\rho P}{K}
Option: 3 \frac{PK}{\rho}  
Option: 4 \frac{\rho K}{P}

Answers (1)

best_answer

\rho=\frac{M}{V}

\begin{array}{l} \frac{\mathrm{d} \rho}{\rho}=-\frac{\mathrm{d} \mathrm{V}}{\mathrm{V}} \\ \mathrm{k}=-\frac{\mathrm{P}}{\frac{\mathrm{d} \mathrm{V}}{\mathrm{V}}} \\ -\frac{\mathrm{d} \mathrm{V}}{\mathrm{V}}=\frac{\mathrm{P}}{\mathrm{k}} \\ \ \\ \frac{\mathrm{d} \rho}{\rho}=\frac{\mathrm{P}}{\mathrm{k}} \\\\ \Rightarrow \mathrm{d} \rho=\frac{\rho \mathrm{P}}{\mathrm{k}} \end{array}

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Deependra Verma

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