Question

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

• A. $\frac{YA{x}^2}{L}$
• B. $\frac{YA{x}^2}{2L}$
• C. $\frac{YA{L}^2}{x}$
• D. $\frac{YA{L}^2}{2x}$

Answer 1

The correct option is B

$\frac{YA{x}^2}{2L}$

Work done, $W=\frac{1}{2}\times Stress\times Strain\times Volume$
We know that, $Stress=Y\times Strain=Y\left(\frac{x}{L}\right)$
$\therefore W=\frac{1}{2}\times Y\left(\frac{x}{L}\right)\times \frac{x}{L}\times AL$
$=\frac{YA{x}^2}{2L}$
Hence, the correct choice is (b).