Question

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

• A. $140m$
• B. $120m$
• C. $75m$
• D. $200m$

Answer 1

The correct option is C $75m$

$\begin{array}{c}\text{Breaking stress}=6\times {10}^{6}N/m^2\\ \text{Density}=8\times {10}^{3}Kg/m^3\end{array}$

$\begin{array}{c}T=Mg\\ T=\left(A\right)\times L\times \rho \times g\\ \frac{T}{A}=\mathrm{stress}=L\rho g\end{array}$

$\text{Breaking stress}=\mathrm{Lmax}\times \rho \times g$

$\begin{array}{cc}6\times {10}^6=& L_{\mathrm{Max}}\times 8\times {10}^3\times 10\\ \mathrm{Lmax}& =\frac{6}{8}\times 100\\ L=75m& \end{array}$