Question

A brass wire of diameter 1 mm and length 2 m is stretched by applying a force of 20 N. If the increase in length is 0.51 mm. Then

• A. stress of the wire is 2.546 x ${10}^{7}N/m^2$
• B. Strain in the wire is 0.255 x ${10}^{-3}$
• C. Young's Modulus of the wire is 0.99 x ${10}^{11}N/m^2$
• D. Stress of the wire is 4.646 x ${10}^{6}N/m^2$

Answer 1

The correct option is C Young's Modulus of the wire is 0.99 x ${10}^{11}N/m^2$

$\begin{array}{c}\text{diameter}=1mm\\ \text{Length}=2m\\ \text{Force}=20N\\ \text{elongation}=0.51mm\end{array}$

$\begin{array}{cc}Y=\frac{\text{Stress}}{\text{Strain}}& =\frac{\text{Force}}{\text{Area}}\times \frac{\text{length}}{\text{elongation}}\\ & =\frac{20}{\pi {(\frac{1}{2}\times {10}^{-3})}^2}\times \frac{2}{0.51\times {10}^{-3}}\\ Y& =0.99\times {10}^{11}N/m^2\end{array}$