Question

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 the amount x. The work done is:

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

Answer 1

Answer: (A)

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

Using Work energy theorem we get:

Work done = Elastic potential energy stored in spring
$=\frac{1}{2}\times Y\times (strain{)}^2\times volume$
$=\frac{1}{2}\times Y\times {\left(\frac{x}{L}\right)}^2\times (A\times L)$
$=\frac{YA{x}^2}{2L}$