A metal rod of length L cross sectional area A young 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
A
`(Ya alphaLt^(2))/(2)`
B
`(Ya alpha^(2)Lt^(2))/(2)`
C
`(Ya alpha^(2)L^(2)t^(2))/(2)`
D
`(Ya alphaLt)/(2)`
Text Solution
Verified by Experts
The correct Answer is:
d
work perfomed by the rod `Delta` w= change in potential energy of the rod ` =1/2xx` stress x strian x volume `=1/2xxyxx("strains")^(2)x"AL"` `=1/2xxyxxalpha^(2) Delta t^(2)xxAL=(YA alpha^(2)Lt^(2))/(2) ["before" Delta L=L alpha t]`
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