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in Physics by (24.5k points)

A metallic wire is suspended by suspending a weight to it. If α be the longitudinal strain and Y its young's modulus of elasticity, show that the elastic potential energy per unit volume is given by (Yα2/2).

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Stress = Young's modulus x strain = Y x α

Elastic potential energy per unit volume is

u = 1/2 x stress x strain = 1/2 x Y x α x α = 1/2 x Y x α2

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