The density and breaking stress of a wire are $6 \times 10^4\mathrm{~kg/m}^3$ and $1.2 \times 10^8\mathrm{~N/m}^2$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $\frac{1}{3}^{\text{rd}}$ of the value on the surface of earth. The maximum length of the wire without breaking is $\_\_\_\_$ m (take, $\mathrm{g} = 10\mathrm{~m/s}^2$).