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If S is the stress and Y is the Young's modulus of the material of a wire, the energy stored in the wire per unit volume is

Asked in AIEEE 2005 · Energy stored in a stretched wire

• (1) (2Y)/S
• (2) S/(2Y)
• (3) 2S²Y
• (4) (S²)/(2Y)

Step-by-step solution

Why the other options are wrong

• (1) comes from is upside down in every respect: energy density must grow with stress and fall with stiffness, while this grows with Y and falls with S.
• (2) comes from stopping at 1/2× strain, that is, writing u=1/2ε and forgetting to multiply by the stress S as well; it is a dimensionless quantity, not an energy density.
• (3) comes from writing u=1/2Sε with ε=SY instead of ε=S/Y, and then losing the factor 1/4; Y belongs in the denominator of the strain.

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