A) \[0.5 Y\,\,{{X}^{2}}\]
B) \[0.5 {{Y}^{2}}\,\,X\]
C) \[2Y\,\,{{X}^{2}}\]
D) \[Y\,{{X}^{2}}\]
Correct Answer: A
Solution :
Elastic potential energy per unit volume \[\operatorname{U}= \frac{1}{2}\,\times stress \times strain\] From definition of Young?s modulus of wire, \[Y=\frac{stress}{strain}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\operatorname{Stress} = Y \times strain\] Given, \[strain=Y\] \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,U\,\,=\,\,\frac{1}{2}\,Y\,{{X}^{2}}\,\,\Rightarrow \,\,\,U\,\,=\,\,0.5\,Y{{X}^{2}}\]
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