A uniform wire of density ρ and breaking stress σ(breaking) hangs vertically under its own weight. No additional mass is attached. Neglect variation of g. What is the maximum possible length of the wire that can hang without breaking?
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Question

A uniform wire of density ρ and breaking stress σ(breaking) hangs vertically under its own weight. No additional mass is attached. Neglect variation of g. What is the maximum possible length of the wire that can hang without breaking?

Options

G1 Physics · Accepted Answer

Maximum tensile stress occurs at the upper end. For a wire of length L and area A, the tension at the top is the weight of the whole wire: T(top) = ρALg. Therefore, σ(top) = T(top)/A = ρLg. At the limiting condition, σ(top) = σ(breaking). Thus, ρL(max)g = σ(breaking). Hence, L(max) = σ(breaking) / [ρg]. An important result is that the maximum self-supporting length is independent of the cross-sectional area. Correct option: A.