Question

wire of length 10 m and cross-sectional are ${10}^{-6}{m}^2$ is stretched with a force of 20N. if the elongation is 1 mm, young's modulus of material of the wire is

• A. ${10}^{10}N{m}^{-2}$
• B. $2\times {10}^{11}N{m}^{-2}$
• C. $2\times {10}^{10}N{m}^{-2}$
• D. $2\times {10}^{-2}$

Answer 1

The correct option is B $2\times {10}^{11}N{m}^{-2}$

$\begin{array}{c}\text{Given length of wire}=10m\\ \text{Cross-sectional area}={10}^{-6}{m}^2\\ \text{Force}=20N\\ \text{Elongation}=\Delta L={10}^{-3}m\end{array}$

$\begin{array}{cc}Y& =\frac{\text{stress}}{\text{strain}}=\frac{\left(F/A\right)}{\left(\Delta l/L\right)}\\ & =\frac{20\times 10}{{10}^{-6}\times {10}^{-3}}\\ Y& =2\times {10}^{11}N{m}^{-2}\end{array}$