Question

The breaking stress of steel is $7.9\times {10}^{9}N{m}^{-2}$ and density of steel is $7.9\times {10}^{3}kg{m}^{-3}$ and $g=10m{s}^{-2}$. The maximum length of steel wire that can hang vertically without breaking is?

• A. ${10}^{3}m$
• B. ${10}^{4}m$
• C. ${10}^{2}m$
• D. ${10}^{5}m$

Answer 1

The correct option is D ${10}^{5}m$

$\begin{array}{cc}& \begin{array}{c}\text{stress,}\sigma =7.9\times {10}^{9}N/m^2\\ \text{density,}\rho =7.9\times {10}^3{N/m}^2\\ \sigma =\frac{\text{its own weight (wire)}}{A}\end{array}\\ & \sigma =\frac{mg}{A}\end{array}$

$\begin{array}{cc}\sigma & =\frac{\left(\rho v\right)g}{A}\\ \Rightarrow \sigma & =\frac{\rho Alg}{A}=\rho lg\end{array}$

$\begin{array}{cc}& \Rightarrow l=\frac{\sigma }{\rho g}=\frac{7.9\times {10}^9}{7.9\times {10}^3\times 10}={10}^{5}m\\ & \text{Ans is (}D)\end{array}$