Question

The breaking stress of the material of a wire is $6 \times 10^{6}\,Nm^{-2}$ 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 (in metre) of the wire made of that material should be (take $54g = 10 \,ms^{-2})$

Answer 1

Breaking stress $=\frac{\text{Force}}{\text{area}}$
The breaking force will be its own weight
$F=mg =V\, \rho g$ = area $\times \,\ell\rho g $
Breaking stress $= 6\times 10^{6} =\frac{area \times\ell\times\rho g}{area} $
or $\ell=\frac{6\times10^{6}}{3\times10^{3}\times10}=200\,m$