Question

If $r$ is the density of the material of a wire and $s$ the breaking stress. The greatest length of the wire that can hang freely without breaking is :

• A. $\frac{2\sigma }{\rho g}$
• B. $\frac{\rho }{\sigma g}$
• C. $\frac{\rho g}{2\sigma }$
• D. $\frac{\sigma }{\rho g}$

Answer 1

The correct option is D $\frac{\sigma }{\rho g}$

Stress = weight/area

$=Al\rho g/A=l\rho g\Rightarrow \sigma =l\rho g$

$\therefore$ $l=\sigma /\rho g$

Hence (D) is correct.