Question

The work done per unit volume to stretch the length of a wire having area of cross-section $5{\text{mm}}^2$ by $4\%$ will be
(Take Young's modulus $Y=8\times {10}^{10}{\text{N/m}}^2$)

• A. $64{\text{MJ/m}}^3$
• B. $32{\text{MJ/m}}^3$
• C. $64{\text{J/m}}^3$
• D. $32{\text{J/m}}^3$

Answer 1

The correct option is A $64{\text{MJ/m}}^3$

The work done is stated as the elastic potential energy or strain energy.
Work done per unit volume in stretching
$U=\frac{1}{2}\times Y\times {\text{(strain)}}^2$
where $Y=$ Young's modulus
$U=\frac{1}{2}\times 8\times {10}^{10}\times {\left(\frac{4}{100}\right)}^2$
$=64\times {10}^6{\text{J/m}}^3$
$=64{\text{MJ/m}}^3$