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  • A wire of length L and cross-sectional area A is made of a material of Young's modulus Y. The work one in stretching the wire by an amount x is given by<div class='qna-option

A wire of length L and cross-sectional area A is made of a material of Young's modulus Y. The work one in stretching the wire by an amount x is given by

Option: 1

\mathrm{\frac{Y A x^2}{L}}


Option: 2

\mathrm{\frac{Y A x^2}{2 L}}


Option: 3

\mathrm{\frac{Y A L^2}{x}}


Option: 4

\mathrm{\frac{Y A L^2}{2 x}}


Answers (1)

best_answer

Work done per unit volume of the wire

\mathrm{ \begin{aligned} & =\frac{1}{2}(\text { stress } \times \text { strain }) . \\\\ Y & =\frac{\text { stress }}{\text { strain }} \\\\ \therefore \quad \text { stress } & =Y \times \text { strain } \end{aligned} }

\therefore \quad Work done per unit volume

\mathrm{ =\frac{1}{2} \times Y \times(\text { strain })^2=\frac{1}{2} \times Y \times\left(\frac{x}{L}\right)^2 }

But, volume of the wire \mathrm{=A \times L}

\mathrm{ \begin{aligned} \therefore \quad \text { Work done } & =\frac{1}{2} \times Y \times\left(\frac{x}{L}\right)^2 \times A \times L \\\\ & =\frac{Y A x^2}{2 L} \end{aligned} }

Posted by

Ritika Harsh

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