A) \[\frac{1}{2}Y\times \] stress x strain \[\times \] volume
B) \[\frac{{{(stress)}^{2}}\times volume}{2Y}\]
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. \[Y=\frac{longitudinal\text{ }stress}{longitudinal\text{ }strain}\] \[\therefore \] \[W=\frac{1}{2}\times \] stress \[\times \frac{stress}{Y}\times \] volume \[=\frac{{{(stress)}^{2}}\times volume}{2Y}\]
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