A) \[\frac{YA{{x}^{2}}}{2L}\]
B) \[\frac{YA{{x}^{2}}}{L}\]
C) \[YA{{x}^{2}}L\]
D) \[\frac{YAx}{2L}\]
Correct Answer: A
Solution :
When a wire is stretched, work is done against interatomic forces which is stored as potential energy in the wire, given by \[U=\frac{1}{2}\times \] force extension \[=\frac{1}{2}F\,x\] ... (i) Also, \[Y=\frac{stress~}{strain~~}=\frac{F/A}{x/L}\] ? (ii) From Eqs. (i) and (ii), we get \[U=\frac{1}{2}\frac{YA\,\,x}{L}\,x=\frac{1}{2}\frac{YA\,{{x}^{2}}}{L}\]
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