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 :
Solution
Bulk modulus $$K = {{ - \Delta P} \over {{{\Delta v} \over v}}} = {{ - \Delta Pv} \over {\Delta v}}$$<br><br>We know, $\rho = {M \over V}$<br><br>So, ${{ - \Delta \rho } \over \rho } = {{\Delta v} \over v}$<br><br>$$K = {{ - \Delta P} \over {\left( { - {{\Delta \rho } \over \rho }} \right)}} = {{\rho \Delta P} \over {\Delta \rho }}$$<br><br>$\Delta \rho = {{\rho \Delta P} \over K}$<br><br>$\Delta \rho = {{\rho P} \over K}$
About this question
Subject: Physics · Chapter: Properties of Solids and Liquids · Topic: Elasticity
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