A) \[0.5 Y{{X}^{2}}\]
B) \[0.5 {{Y}^{2}}X\]
C) \[2 Y{{X}^{2}}\]
D) \[{{\operatorname{YX}}^{2}}\]
Correct Answer: A
Solution :
Elastic potential energy per unit volume \[\operatorname{U} = \frac{1}{2}\times Stress \times Strain\] \[\operatorname{U} = \frac{1}{2}\times Y\times Stress \times Strain\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( \because \,\,\,Y=\frac{Stress}{Strain} \right)\] \[= \frac{1}{2}\times Y\times {{\left( Strain \right)}^{2}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( \because \,\,\,Y=\frac{Stress}{Strain} \right)\] \[U=(0.5)Y{{X}^{2}}\]
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