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) \[\frac{h\rho g}{\sigma }\]
Correct Answer: A
Solution :
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 \[u=\frac{1}{2}\times \text{compressibility}\,\text{ }\!\!\times\!\!\text{ }\,{{\text{(stress)}}^{\text{2}}}\] \[\because \] \[\text{Stress}=h\,e\,g\] \[\therefore \] \[u=\frac{1}{2}\sigma {{(h\,e\,g)}^{2}}\]
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