A) \[\frac{\text{1}}{\text{2}}\text{Y}\,\text{ }\!\!\times\!\!\text{ }\,\text{stress}\,\text{ }\!\!\times\!\!\text{ strain}\,\text{ }\!\!\times\!\!\text{ }\,\text{volume}\]
B) \[\frac{{{\text{(stress)}}^{\text{2}}}\text{ }\!\!\times\!\!\text{ }\,\text{volume}}{\text{2Y}}\]
C) \[stress\times strain\times volume\]
D) \[Y\times \frac{{{(stress)}^{2}}}{volume}\]
Correct Answer: B
Solution :
When a wire is stretched work is done against the interatomic forces. This work is stored in the wire in the form of elastic potential energy. \[W=\frac{1}{2}\times \]stress \[\times \] strain \[\times \] volume of wire Also when strain is small, ratio of longitudinal stress to corresponding longitudinal strain is called Youngs Modulus of material of body. \[\text{Y = }\frac{\text{longitudinal}\,\text{stress}}{\text{longitudinal}\,\text{strain}}\] \[\therefore \] \[\text{W = }\frac{\text{1}}{\text{2}}\text{ }\!\!\times\!\!\text{ stress }\!\!\times\!\!\text{ }\frac{\text{stress}}{\text{Y}}\text{ }\!\!\times\!\!\text{ volume}\] \[\text{=}\frac{{{(stress)}^{2}}\times volume}{2Y}\]
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