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Let a wire be suspended from the ceiling (rigid support) and stretched by a weight W attached at its free end. The longitudinal stress at any point of cross-sectional area A of the wire is:
At any cross-section, equilibrium requires internal tension T = W. Therefore, longitudinal stress = T / A = W / A in 5 seconds!
When an external deforming force is applied to a body, an internal restoring force equal in magnitude and opposite in direction develops within the material across every plane of cross-section. Stress σ is defined as this internal restoring force per unit area:
For a wire of negligible mass suspended from a rigid ceiling and carrying a weight W at its free end, make an imaginary horizontal cut at any point along the wire. For the lower portion to remain in static equilibrium, the internal tension T across the cross-sectional area A must balance the weight W:
Substituting the internal restoring tension into the stress formula:
Diagnose every choice: Know exactly why the right option works and why distractors fail.
Wire is under tension; stress cannot be zero.
Spurious factor of 2.
Exact canonical formula for longitudinal tensile stress.
Unwarranted division by 2.
If a heavy wire stretches under its OWN weight, the average stress is W_wire / 2A. But for a light wire carrying a concentrated weight W at the end, the tension is UNIFORM throughout and equals W everywhere ⟹ Stress = W / A.
"Longitudinal stress is internal restoring force per unit area: σ = W / A."
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