Physics - Elasticity Question with Solution | TestHub

From the definition of bulk modulus

$\text{B}=-\frac{\text{dp}}{\frac{\text{dV}}{\text{V}}}$

As we move from surface to place where pressure changes to$\alpha {\text{p}}_0$, let us assume volume changes by$\Delta \text{V}$, then

$\text{B}=-\frac{\text{V}\Delta \text{p}}{\Delta \text{V}}=\frac{\text{V}\left(\alpha -1\right){\text{p}}_0}{\Delta \text{V}}$

New volume,${\text{V}}^{\prime }=\text{V}-\Delta \text{V}=\left[1-\frac{\left(\alpha -1\right){\text{p}}_0}{\text{B}}\right]\mathrm{V}$

Density at the given depth,${\rho }^{\prime }=\rho \frac{\text{V}}{{\text{V}}^{\prime }}$, where$\rho$is density at surface

${\rho }^{\prime }=\frac{\rho \times \text{B}}{\text{B}-\left(\alpha -1\right){\text{p}}_0}$