Question

The length of a copper wire increases by 0.01 metre when loaded with 10kg weight. Another copper wire of the same length but double the radius is loaded with the same weight. The increase in length of the second wire in metres will be

• A. 0.002
• B. 0.005
• C. 0.0025
• D. 0.01

Answer 1

The correct option is C 0.0025

$\begin{array}{c}\text{Given,}\\ \text{increase in length}\left(\Delta L\right)=0.01m\\ \text{when load is}\\ \text{Let length}=Lm\\ \text{radius}=r\end{array}$

$\text{young's modulus}=\frac{\text{Stress}}{\text{strain}}$

$\begin{array}{c}y=\frac{\left(\frac{F}{A}\right)}{\left(\frac{\Delta L}{L}\right)}\\ y=\frac{10\times 10\times L}{\pi r^2\times 0.01}\end{array}$

$y=\frac{{10}^{4}L}{\pi r^2}-\cdots \left(1\right)$

$\begin{array}{c}\text{when,}\\ \begin{array}{c}r\text{becomes}2r\\ \text{Load remains same}\end{array}\end{array}$

$TY=\frac{FL}{4\pi r^2(\Delta L{)}_{\text{new}}}---\left(11\right)$

$\begin{array}{cc}\text{(i)}=& \text{(ii)}\\ & \frac{{10}^{4}L}{\pi r^2}=\frac{{10}^{2}L}{4\pi r^2}(\Delta L{)}_{\text{new}}\end{array}$

$\begin{array}{cc}(\Delta L{)}_{\text{new}}& =\frac{1}{400}m\\ \Delta L& =0.0025m\end{array}$