Question

A steel is 1 m long and $1m{m}^2$ in area of cross-section .If it takes 200 N to stretch this wire by 1 mm , how much force will be required to stretch a wire of the same material as well as diameter from its normal length of 10 m to a length of 1002 cm ?

• A. 1000 N
• B. 200 N
• C. 400 N
• D. 2000 N

Answer 1

Answer: (C)

400 N

$\begin{array}{c}\text{Given,}\\ \text{A steel wire}\\ \begin{array}{c}\text{Length}\left(L\right)=1m\\ \text{Area}\left(A\right)=1m{m}^2=1\times {10}^{-6}{m}^2\\ \text{- it takes}200N\text{and}\Delta L=1mm={10}^{-3}m\\ \text{From above data,}\end{array}\end{array}$

$\begin{array}{cc}\text{Young modulus}& =\frac{\text{stress}}{\text{strain}}\\ & =\frac{FL}{A\Delta L}\\ & =\frac{200\times 1}{{10}^{-6}\times {10}^{-3}}\\ y& =2\times {10}^{11}N/m^2\end{array}$

$\begin{array}{c}\text{when}L=10m\\ \begin{array}{cc}\Delta L& =2cm=0.02m\\ F& =?\\ \text{we know}& \\ y=\frac{FL}{A\Delta L}& \end{array}\\ \begin{array}{cc}F& =\frac{yA\Delta L}{L}\\ & =\frac{2\times {10}^{11}\times {10}^{-6}\times 0.02}{10}\\ F& =400N\end{array}\end{array}$