A wire has a breaking stress of 6 × 10 ^ 5 Nm^ - 2 ~and a density...

Given: Breaking stress& $= 6 \times {10}^{5}Nm^{- 2}$.

Density~$ρ = 3 \times {10}^{4}kgm^{- 3}$.

Stress is the ratio of force acting on a unit area of an object given as~$Stress = \dfrac{F}{A}$.

We~know that force is given as~$F =$mass $\times$acceleration.

Thus, breaking stress~$= \dfrac{mg}{A}$.

Since, density is stated as~$= \dfrac{mass}{volume}$, so~$m = ρV = ρAL$.

Putting in stress formula, we get~$Stress = \dfrac{ρALg}{A} = ρLg$

$6 \times {10}^{5} = 3 \times {10}^{4} \times L \times 10⇒ L = 2m$

Hence, the length of the wire is~$2m$.