a steel wire of dia 4mm has a breaking stress of 4x10^5N find the vreaking stress for a similar wire of dia 2mm
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The breaking stress of a similar wire of diameter 2 mm is 10⁵ N
we know that the breaking stress is directly proportional to area ,
F ∝ A = πD²/4
Hence the breaking stress is directly proportional to square of the diameter.
=> F ∝ D²
=> F₂/F₁ = D₂²/D₁² = (2/4)² = 1/4
=> F₂ = F₁/4 = 4 x 10⁵/4 = 1 x 10⁵ N
Hence the breaking stress of a similar steel wire of diameter 2 mm is 10⁵ N
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