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Which of the following correctly gives t...

Which of the following correctly gives the elastic energy stored in the metal bar ? `(sigma= "stress,"" " epsi= "strain"," "Y=Young's" " "modulus," "L= lenght", " "Deltal = "extension, " " F= load", " "A= "cross -sectionl" "area").

A

`(1)/(2)sigma^(2)Y`

B

`(1)/(2)(sigma^(2))/(Y)`

C

`(1)/(2)epsi^(2)Y.(AL)`

D

`(1)/(2)sigma^(2)Y.(AL)`

Text Solution

Verified by Experts

The correct Answer is:
C
(c) Energy stored `=(1)/(2)xx "stress"xx"strain"xx"volume"=(1)/(2)xxsigmaxxepsixx(AL)`
As, `Y=(sigma)/(epsi)implies sigma=epsiY`
So, `E=(1)/(2) epsi^(2)Y.(AL)`
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