Question

Stress developed in the stretched copper wire is $6\times {10}^5{\text{N/m}}^2$. If young's modulus of copper wire is $1.2\times {10}^{11}{\text{N/m}}^2$, find the energy stored per unit volume in the stretched wire.

• A. $0.5{\text{J/m}}^3$
• B. $1.5{\text{J/m}}^3$
• C. $2.5{\text{J/m}}^3$
• D. $3{\text{J/m}}^3$

Answer 1

The correct option is B $1.5{\text{J/m}}^3$

We know, energy stored per unit volume in a wire is given by
$\therefore \Delta U=\frac{1}{2}\times \left(\text{stress}\right)\times \left(\text{strain}\right)$
$\Rightarrow \Delta U=\frac{1}{2}\times \frac{(\text{stress}{)}^2}{Y}$ $[\because Y=\frac{\text{stress}}{\text{strain}}]$
$\Rightarrow \Delta U=\frac{1}{2}\times \frac{(6\times {10}^5{)}^2}{1.2\times {10}^{11}}$
$\Rightarrow \Delta U=1.5{\text{J/m}}^3$