A force of $$6 \times {10^6}\,N{m^{ - 2}}$$   is required for breaking a material. Then density $$\rho $$ of the material is $$3 \times {10^3}\,kg\,{m^{ - 3}}.$$    If the wire is to break under its own weight, the length of the wire made of that material should be (take $$g = 10\,m{s^{ - 2}}$$  )

Solution :
Breaking stress $$ = \frac{{{\text{Force}}}}{{{\text{area}}}}$$
The breaking force will be its own weight.
$$F = mg = V\rho g = {\text{area}} \times \ell \rho g$$
Breaking stress $$ = 6 \times {10^6} = \frac{{{\text{area}} \times \ell \times \rho g}}{{{\text{area}}}}$$
$${\text{or}}\,\,\ell = \frac{{6 \times {{10}^6}}}{{3 \times {{10}^3} \times 10}} = 200\,m.$$