Question

A substance breaks down under a stress of 105 Pa. if the density of the wire 2 × 103kg/m3,findthe minimum length of the wire which will break under its own weight (g = 10m/s2)

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Answer 1

Stress = F/A = {(M ∙ g) / A} (1)

∵ density = [{mass} / {volume}]

ρ = {M / (A ∙ L)} i.e. M = ρAL

∴ from (1)

Stress = {(ρAL ∙ g) / A}

Stress = ρ ∙ L ∙ g

Given : stress = 106 N/m2

ρ = 3 × 103 kg/m3

Hence

106 = 3 × 103 × L × 10

∴ {106 / (3 × 104)} = L

∴ L = (100 / 3)

L = 33.3 m