# If $\rho$ is density of the material of a wire and $\sigma$ is the breaking stress. The greatest length of wire that can hang freely without breaking is

$\begin {array} {1 1} (a)\;\frac{2 \sigma}{\rho g} \\ (b)\;\frac{\rho}{\sigma g} \\ (c)\;\frac{\rho g}{2 \sigma} \\ (d)\;\frac{\sigma}{\rho g}\end {array}$

Maximum stress will be at the point of suspension.
Stree $=\large\frac{weight}{Area}$
Let L be the maximum length that can be hing .
$\sigma = \Large\frac{AL\rho g}{A}$
$L= \large\frac{\sigma}{\rho g}$
Hence d is the coprrect answer.

edited Feb 18, 2014 by meena.p