Question

The length of the wire increases 8 mm when a weight of 5 kg is hung. If all conditions are same, but the radius of the wire is doubled, what will be the increase in its length?

• A. 2 mm
• B. 1 mm
• C. 0.5 m
• D. 1.5 mm

Answer 1

Answer: (A)

2 mm

$\begin{array}{cc}\text{Elongation}& =8mm\\ \text{Weighting}& =5kg\end{array}$

$\begin{array}{c}\text{Let}r\text{be radius and}l\text{be length.}\\ \begin{array}{c}\Delta l=\frac{\left(5g\right)\times 1}{\left(\pi r^2\right)\times Y}\text{is the formula}\\ \Rightarrow 8\times {10}^{-3}=\frac{\left(5g\right)L}{\left(\pi r^2\right)\times Y}⟶\left(1\right)\end{array}\end{array}$

$\begin{array}{c}\text{Given radius is doubled keeping all parameters same.}\\ \text{Now new elongation}e:\\ e=\frac{\left(5g\right)\times L}{\left(\pi \right(2r{)}^2)\times y}⟶\left(2\right)\end{array}$

$\begin{array}{c}\text{Now (1)}/\left(2\right)\\ \end{array}$

$\begin{array}{c}\frac{8\times {10}^{-3}}{e}=\frac{5gl}{\pi x^2-4}\times \frac{4\pi r^{2}Y}{5gl}\\ E=2mm\end{array}$