Question

Given $ \sigma $ is the compressibility of water, $ \rho $ is the density of water arid k is the bulk modulus of water. What is the energy density of water at the bottom of a lake $ h $ metre deep?

• A. $ \frac{1}{2}\sigma {{(h\rho g)}^{2}} $
• B. $ \frac{1}{2}\sigma (h\rho g) $
• C. $ \frac{1}{2}\frac{h\rho g}{\sigma } $
• D. $ \frac{h\rho g}{\sigma } $

Answer 1

Answer: (A)

Energy density, $ u=\frac{1}{2}\times \text{stress }\!\!\times\!\!\text{ strain} $
$ u=\frac{1}{2}\times \text{stress}\,\text{ }\!\!\times\!\!\text{ }\,\frac{\text{stress}}{\text{Bulk}\,\text{modulus}} $
or $ u=\frac{1}{2}\times \text{compressibility}\,\text{ }\!\!\times\!\!\text{ }\,{{\text{(stress)}}^{\text{2}}} $
$ \because $ $ \text{Stress}=h\,e\,g $
$ \therefore $ $ u=\frac{1}{2}\sigma {{(h\,e\,g)}^{2}} $