A wire has a breaking stress of 6 × 10 5   N   m - 2 and a density of 3 × 10 4   kg   m - 3 . The length of the wire of the same material will break under its own weight if g = 10   m   s - 2 is

Step-by-step solution

Given: Breaking stress = 6 × 10 5   N   m - 2 . Density ρ = 3 × 10 4   kg   m - 3 . Stress is the ratio of force acting on a unit area of an object given as Stress = F A . We know that force is given as F = mass × acceleration. Thus, breaking stress = m g A . Since, density is stated as = mass volume , so m = ρ V = ρ A L . Putting in stress formula, we get Stress = ρ A L g A = ρ L g 6 × 10 5 = 3 × 10 4 × L × 10 ⇒ L = 2   m He