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If in a wire of Young's moduls Y, longit...

If in a wire of Young's moduls `Y`, longitudinal strain `X` is produced then the potential energy stored in its unit volume will be:

A

`xy^2`

B

`2xy^2`

C

`(1)/(2)y^2x`

D

`(1)/(2)yx^2`

Text Solution

Verified by Experts

The correct Answer is:
D
Energy stored per unit volume `=(1)/(2)xx`stress`xx`strain
From the difinition of Young's modulus of wire
`Y=(stress)/(strai n)`
`impliesstress=Yxxstrai n`
Given, strain`=X`
Therefore, `U=(1)/(2)XX`Young's modulus `xx(strai n)^2`
`=(1)/(2)xxYxx x^2`
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Knowledge Check

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