Question

A wire of length 5 m and radius 1 mm is stretched by load of 10 N. If Y = 2 x ${10}^{11}N/m^2$, find the work done per unit volume of the wire.

• A. 2.35 $J/m^3$
• B. 2.535 $J/c{m}^3$
• C. 25.35 $J/m{m}^3$
• D. 253.5 $J/m^3$

Answer 1

The correct option is C 25.35 $J/m{m}^3$

$\begin{array}{c}\text{Enery stored inside wire = Work done}\\ U=\frac{1}{2}\times \text{stress}x\text{strain}x\vee \end{array}$

$\begin{array}{c}\text{Work done per unit valura}\\ \frac{0}{v}=\frac{1}{2}x\text{stress}x\text{strain}\end{array}$

$\begin{array}{c}=\frac{1}{2}x\frac{(s+\gamma es){)}^2}{r}\\ =\frac{1}{2}\times \frac{F^2}{A^{2}y}=\frac{1}{2}\times \frac{100}{2\times {10}^{11}\times {\pi }^2\times {10}^{-12}}\\ =\frac{250}{{\pi }^2}=25.35J/m^3\end{array}$