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A metal rod of length 'L', cross-section...

A metal rod of length 'L', cross-sectional area 'A', Young's modulus 'Y' and coefficient of linear expansion `'alpha'` is heated to `'t'^(@)C`. The work that can be perfomred by the rod when heated is

A

`(Y A alpha Lt^(2))/(2)`

B

`(YA alpha^(2) L t^(2))/(2)`

C

`(YA alpha^(2) L^(2) t^(2))/(2)`

D

`(YA alpha Lt)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`W= (1)/(2) xx` (Stress) `xx` Strain `xx` Volume
`W= (1)/(2) xx Y xx ("Strain")^(2) xx AL`
`(Delta L)/(L) = alpha Delta t= alpha t`
`W= (1)/(2) xx Y xx (alpha t)^(2) xx AL = (1)/(2) Y A alpha^(2) Lt^(2)`
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