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

Question

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