Question

A wire has a breaking stress of $6\times {10}^{5}N/m^2$ and a density of $3\times {10}^{4}kg/m^3$. The length of the wire of the same material which will break under its own weight, (if g = 10 m/s${}^2$) is :

• A. 2000 m
• B. 2500 m
• C. 20 m
• D. 2 m

Answer 1

The correct option is D 2 m

Breaking stress is given by $\frac{mg}{A}$

The given breaking stress $=6\times {10}^{5}N/m^2$
$\therefore 6\times {10}^{5}N/m^2=\frac{mg}{A}$ (But $m=AL\rho$)
Or $6\times {10}^5=\frac{AL\rho g}{A}=L\rho g$
Thus, $L=\frac{6\times {10}^5}{\rho g}=\frac{6\times {10}^5}{3\times {10}^4\times 10}=2m$