The breaking stress for a metal is $7.8\times {10}^9{\mathrm{Nm}}^{-2}$ . The density of the metal is $7800{\mathrm{kgm}}^{-3}$. If $g=10\mathrm{N}{\mathrm{kg}}^{-1}$, Find the maximum length of the wire (in km) made of this metal which may be suspended without breaking.

If L is the maximum length of the wire that can be suspended.

Then, $F=mg\text{, }$where $m=\rho LA$ (where A- cross-sectional area)

$\therefore \text{ Maximum stress }=\frac{\mathrm{mg}}{\mathrm{A}}=\mathrm{g}\cdot \frac{\mathrm{\rho LA}}{\mathrm{A}}=\mathrm{\rho Lg}$

$\text{ Given, breaking stress }{\rho }_b=7.8\times {10}^9{\mathrm{Nm}}^{-2}$

$\begin{array}{l}\therefore \mathrm{\rho Lg}=7.8\times {10}^9\Rightarrow \mathrm{L}=7.8\times {10}^9\times \frac{1}{7800\times 10}\\ \text{ or }\mathrm{L}={10}^5\mathrm{m}=100\mathrm{km}\end{array}$