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A metallic wire is stretched by suspendi...

A metallic wire is stretched by suspending weight from it if `alpha` is the longitudinal strain & y is the young's modulus, show that elastic potential energy per unit volume is given by `(1)/(2)yalpha^(2)`.

Text Solution

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Elastic P.E. per unit volume
`U = (1)/(2) "stress" xx "strain"`
`Y = ("stress")/("strain") = ("stress")/(alpha)`
Hence, `U = (1)/(2) xx y alpha xx alpha = (1)/(2)y alpha^(2)`
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