Question

A wire of length 10m and area of cross section 2 sq. mm is stretched by a load of 1 kg weight. An elongation of 0.001% is produced. The young's modulus of the material of the wire is

• A. $49\times {10}^{11}N/m^2$
• B. $4.9\times {10}^{11}N/m^2$
• C. $9.8\times {10}^{11}N/m^2$
• D. $98\times {10}^{11}N/m^2$

Answer 1

The correct option is B $4.9\times {10}^{11}N/m^2$

$\begin{array}{c}\text{Given,}\\ \text{Length of wire}\left(L\right)=10m\\ \text{cross section}\left(A\right)=2{mm}^2=2\times {10}^{-6}{m}^2\\ \text{Loa d}\left(m\right)=1kg\\ \text{So, Force}=mg\\ =1\times 10\\ =10N\end{array}00$

$\begin{array}{c}\text{and}\frac{\Delta L}{L}\times 100=0.001(\Delta L=\text{elongation})\\ \frac{\Delta L}{L}=1\times {10}^{-5}\end{array}$

$\begin{array}{c}\text{we know,}\\ \text{young's modulus}=\frac{\text{Stress}}{\text{strain}}\end{array}$

$\begin{array}{c}=\frac{\left(\frac{F}{A}\right)}{\left(\frac{\Delta L}{L}\right)}\\ =\frac{\frac{10}{2\times {10}^{-6}}}{1\times {10}^{-5}}\end{array}$

$Y=4.9\times {10}^{11}N/m^2$