Question

A steel wire of mass 3.16 kg is stretched to a tensile strain of $1\times {10}^{-3}$. What is the elastic deformation energy if density p=7.9g/cc and Y=$2\times {10}^{11}N/m^2$

• A. 4 KJ
• B. 0.4 KJ
• C. 0.04 KJ
• D. 4 J

Answer 1

The correct option is C 0.04 KJ

$\begin{array}{c}\frac{\Delta l}{l}=1\times {10}^{-3}\\ Y=2\times {10}^{11}N/m^2\\ \rho =7.9g/{cm}^3\end{array}$

$\text{mass of steelwire}=3.16kg$

$\begin{array}{cc}\text{Elastic deformation Energy}& =\text{Energy density}\times \text{volume}\\ & =\frac{1}{2}Y(\text{strain}{)}^2\times \frac{m}{\rho }\\ & =\frac{1}{2}\times 2\times {10}^{11}\times {10}^{-6}\times \frac{3.16}{7900}\\ & =4\times {10}^{-4}\times {10}^5\\ & =40\text{Joules.}\end{array}$