question_answer

A wire of length L and cross sectional area A is made of a material of young's modulus Y. If the wire is stretched by an amount x, the work done is:

A) \[\frac{YA{{x}^{2}}}{2L}\]                

B) \[\frac{YAx}{2{{L}^{2}}}\]   

C) \[\frac{YAx}{2L}\]                    

D) \[\frac{YA{{x}^{2}}}{L}\]

Correct Answer: D

Solution :

\[Stress\,=\frac{F}{A}Strain\,=\frac{x}{\ell }\]                 \[\frac{W}{V}=\frac{1}{2}\,\,\,stress\,\times \,strain\,=\frac{1}{2}\times Y\times {{(strain)}^{2}}\] \[\frac{W}{V}=\frac{1}{2}\times Y\times \frac{{{x}^{2}}}{{{L}^{2}}}\] \[W=\frac{1}{2}\times Y\times \frac{{{x}^{2}}}{{{L}^{2}}}.VV=Ax\] \[W=\frac{Y{{x}^{2}}}{2{{L}^{2}}}AL\] \[W=\frac{Y{{x}^{2}}}{2L}AL\]