Question

A wire whose cross-sectional area id $4m{m}^2$ is stretched by $0.1$mm by a certain load. If a similar wire of double the area of cross-section is under the sane load, then the elongation would be

• A. 0.5 mm
• B. 0.05 mm
• C. 0.005 mm
• D. 5 mm

Answer 1

The correct option is B 0.05 mm

$\begin{array}{c}\text{Given all parameter's are some except area of crosssection}\\ \text{given}{A}_2=2A_1\end{array}$

$\begin{array}{c}\text{Formula,}\\ \begin{array}{cc}Y& =\frac{FL}{Ae}\\ \Rightarrow & e\propto \frac{1}{A}\\ & \frac{e_1}{e_2}=\frac{A_2}{A_1}\\ e_2& =\left(0.1\right)\times \frac{4}{8}\\ & e_2=0.05mm\end{array}\end{array}$