A uniform steel wire of density 8000 kg m ⁻³ has a breaking stress of 4.8 10^8 N m ⁻² . It is suspended vertically from a rigid support. What is the maximum length of the wire that can hang without breaking under its own weight? (Take g = 10 m s ⁻² )

Step-by-step solution

The wire will experience the maximum tension at its highest point (the point of suspension) due to the weight of the entire wire below it. Let the maximum length of the wire be L and its cross-sectional area be A . Mass of the wire, M = Volume Density = A L Maximum tension at the support, T_ = Mg = A L g The stress at the highest point is: Stress = T_ A = A L g A = L g For the wire not to break, this stress must be equal to the breaking stress : = L g L = g Substitute the given values ( = 4.8 10^8 N m ⁻² , = 8000 k