Question

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 :

• A. $\frac{\rho K }{ P }$
• B. $\frac{\rho P }{ K }$
• C. $\frac{ K }{\rho P }$
• D. $\frac{ PK }{\rho}$

Answer 1

Answer: (B)

$\rho=\frac{ M }{ V }$
$\frac{ d \rho}{\rho}=-\frac{ d V }{ V }$
$k =-\frac{ P }{\frac{ d V }{ V }}$
$-\frac{ d V }{ V }=\frac{ P }{ k }$
$\frac{ d \rho}{\rho}=\frac{ P }{ k } \Rightarrow d \rho=\frac{\rho P }{ k }$