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 performed by the rod when heated is

Options

A. `(Y A alpha L t^(2))/(2)`
B. `(Y A alpha^(2) Lt^(2))/(2)`
C. `(YA alpha^(2) L^(2)t^(2))/(2)`
D. `(YA alpha Lt)/(2)`

Answer

B

Explanation

`y=("stress")/("strain")`
`therefore " stress"=y " strain" `
`(F)/(A) =y xx (l)/(L) = y prop t`
`therefore F=(yA prop t`
`W=(1)/(2)F l`
`=(1)/(2) xx y xx A prop t xx prop t L`
`=(1)/(2) xx y xx A prop^(2) t^(2)L`.