Question

A steel wire of mass $3.16Kg$ is stretched to a tensile strain of 1 x 10${}^{-3}$. What is the elastic deformation energy if density $\rho =7.9g/cc$ and Y$=$2x10${}^{11}$ N/m${}^2$?

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

Answer 1

Answer: (C)

$0.04KJ$

$Volume=\frac{mass}{\rho }$
$Y=\frac{stress}{strain}$
$stress=Y\times strain$
$energy=\frac{1}{2}\times stress\times strain\times volume$
$=\frac{1}{2}\times Y\times strain\times strain\times \frac{mass}{\rho }$
$=\frac{1}{2}\times 2\times {10}^{11}\times 1\times {10}^{-3}\times 1\times {10}^{-3}\times \frac{3.16}{7.9\times 1000}$
$=0.04KJ.$