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A metallic wire is stretched by suspendi...

A metallic wire is stretched by suspending weight to it. If `alpha` is the longitudinal strain and Y its Young's modulus of elasticity, shown that the elastic potential energy per unit volume is given by `Y alpha^(2)//2`

Text Solution

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Stress = Young's modulus `xx` strain `=Yxx alpha`
Elastic potential energy per unit volume is
`(DeltaU)/("Volume")=(1)/(2)"stress"xx"strain"`
`=(1)/(2)xx Y alpha xx alpha=(1)/(2)Y alpha^(2)`
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