Question

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

Answer 1

Answer: 100

If $L$ is the maximum length of the wire that can be suspended.
Then, $F=mg$, where $m=\rho LA$ (where $A=$ cross-sectional area)

$\therefore$ Maximum stress $=\frac{mg}{A}=g\cdot \frac{\rho LA}{A}=\rho Lg$
Given, breaking stress ${\rho }_b=7.8\times 10^{9}N{m}^{-2}$
$\therefore \rho Lg=7.8\times 10^9$
$\Rightarrow L=7.8\times 10^9\times \frac{1}{7800\times 10}$
or $L=10^{5}m=100km$