Question

what is the length of a wire that breaks under its own weight when suspended vertically ?
Breaking stress =5*10^7 N/m^3
Density of material of wire=3*10^3 kg/m^3

Answer 1

answer : 1.67 km

Let L is the length of the wire,

M is mass of wire and A is cross sectional area of wire.

we know, stress = force/area

so, stress = Mg/A

we know, mass = density × volume

= d × AL [ density = cross sectional × length = AL ]

so, stress = dALg/A = dLg

here, d = 3 × 10³ kg/m³ , g = 10m/s²

and stress = 5 × 10^7 N/m²

so, 5 × 10^7 = 3 × 10³ × L × 10

or, L = 5 × 10³/3 = 1.67 × 10³m or 1.67km