Question

A steel wire $2m$ in length is stretched by $1mm$. The cross-sectional area of the wire is $2m{m}^2$. If Young's modulus of steel is $2\times {10}^{11}N/m^2$, then the elastic potential energy stored in the wire is

• A. $0.1J$
• B. $0.2J$
• C. $0.3J$
• D. $0.4J$

Answer 1

The correct option is A $0.1J$

given, Steel wire length

$=2m$

$Area=2{mm}^2$

Young modulus of steel $=2\times {10}^{11}$

Using the spring equivalent concept: $\begin{array}{cc}U& =\frac{1}{2}K(\Delta L{)}^2\text{where}K=\frac{YA}{L}\\ & =\frac{1}{2}\left(\frac{YA}{L}\right)(\Delta L{)}^2\\ & =\frac{1}{2}\times (\frac{2\times {10}^{11}\times {10}^{-6}\times 2}{2}\left({10}^{-6}\right)\\ U& =0.1J\end{array}$ Elastic potential energy stored is $\underset{–}{0.1I}$