The density of a metal at normal pressure is $\rho$. Its density when it is subjected to an excess pressure $p$ is $\rho^{\prime}$ If $B$ is Bulk modulus of the metal, the ratio of $\frac{{\rho '}}{\rho }$ is
NEET 2017, Medium
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$B =- V \frac{ dP }{ dV }$
Thus, $\Delta V =-\frac{ pV }{ B }$ or $V ^{\prime}- V =-\frac{ pV }{ B }$ Or, $V^{\prime}=V\left(1-\frac{p}{B}\right)$
Now, $\rho^{\prime}=\frac{ m }{ V ^{\prime}}=\frac{ m }{ V \left(1-\frac{ P }{ B }\right)}=\frac{\rho}{\left(1-\frac{ p }{ B }\right)}$
$\frac{\rho^{\prime}}{\rho}=\frac{1}{\left(1-\frac{ p }{ B }\right)}$
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