The density and breaking stress of a wire are 6×10⁴ kg m⁻³ and 1.2×10⁸ N m⁻² respectively. The wire is suspended from a rigid support on a planet where the acceleration due to gravity is 1/3 of the value on the surface of the earth. The maximum length of the wire without breaking is m. (Take g=10 m…

Question

The density and breaking stress of a wire are 6×10⁴ kg m⁻³ and 1.2×10⁸ N m⁻² respectively. The wire is suspended from a rigid support on a planet where the acceleration due to gravity is 1/3 of the value on the surface of the earth. The maximum length of the wire without breaking is m. (Take g=10 m s⁻²)

Accepted Answer

600. Idea: a hanging wire is most stressed at the top, where the whole of its own weight acts on the cross-section. For a wire of area A and length L, the weight is ρ ALgₚ, so the stress at the support is (ρ ALgₚ)/A=ρ Lgₚ; the area cancels and only the length matters. Here gₚ=g/3=(10)/3 m s⁻² and ρ=6×10⁴ kg m⁻³, so ρ gₚ=6×10⁴×(10)/3=2×10⁵ N m⁻³. Setting ρ gₚL=1.2×10⁸ gives L=(1.2×10⁸)/(2×10⁵). L=600 m.

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