Find the elastic potential energy per unit volume of water $\left(\text{ in }\times {10}^3{\mathrm{Jm}}^{-3}\right)$ at a depth of 1 km. Given, compressibility of water $=5\times {10}^{10}$ SI units and density of water =$1000{\mathrm{kgm}}^{-3}$.

$\text{ Energy per unit volume }=\frac{1}{2}\left(\text{ stress }\right)\left(\text{ strain }\right)$

                $\begin{array}{l}\mathrm{u}=\frac{\mathrm{U}}{\mathrm{V}}=\frac{1}{2}\left(\mathrm{stress}\right)\left(\frac{\mathrm{stress}}{\text{ Bulk modulus }}\right)\\ =\frac{1}{2}(\mathrm{\rho gh}{)}^2\text{ (Compressibility) }\\ =\frac{1}{2}(1000\times 9.8\times 1000{)}^2\left(5\times {10}^{-10}\right)\\ =2.4\times {10}^4{\mathrm{Jm}}^{-3}=24\times {10}^3{\mathrm{Jm}}^{-3}\end{array}$