A uniform wire stores elastic strain energy U when it is stretched gradually by a tensile force F. A second wire made of the same material has twice the length and half the cross-sectional area, and is stretched gradually by force 2F. What elastic strain energy is stored in the second wire?
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Question

A uniform wire stores elastic strain energy U when it is stretched gradually by a tensile force F. A second wire made of the same material has twice the length and half the cross-sectional area, and is stretched gradually by force 2F. What elastic strain energy is stored in the second wire?

Options

G1 Physics · Accepted Answer

For a uniform linearly elastic wire, U = [F²L] / [2AY]. Thus, U ∝ [F²L] / A for the same material. For the second wire, F' = 2F, L' = 2L, A' = A/2. Therefore, U'/U = [(2F)²(2L)/(A/2)] / [F²L/A]. The factors give U'/U = 4×2×2 = 16. Hence, U' = 16U. Correct option: D.