Question

For the breaking stress is $6\times {10}^{6}N/m^2$ and the density is $8\times {10}^{3}N/m^2$ . The maximum length of steel wire , which can be suspended without breaking under its own weight is [$g=10m/s^2$

• A. 140m
• B. 150m
• C. 75m
• D. 200m

Answer 1

The correct option is C 75m

$\begin{array}{cc}& \text{Given,}\\ & \text{Maximum stress}=6\times {10}^{6}N/m^2\\ & \begin{array}{c}\text{Breaking stress or Maximum}\\ \text{density}=8\times {10}^{3}N/m^2\end{array}\end{array}$

$\begin{array}{c}\text{Let, L is length of wire}\\ A\text{is}\text{Area of wire}\\ \text{then mass of wire}=(f\times \text{volume})g\\ \text{weight due to own}=\\ (f\times A\cdot L)g\end{array}$

$\begin{array}{cc}\text{Now,}& \\ \text{stress}& =\frac{F}{A}\\ 6\times {10}^6& =\frac{\rho ALg}{A}\\ L& =\frac{6\times {10}^6}{8\times {10}^3\times 10}\\ L& =75m\end{array}$