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A metallic rod of length l and cross-sec...

A metallic rod of length l and cross-sectional area A is made of a material of Young's modulus Y. If the rod is elongated by an amount y,then the work done is proportional to

A

`(YA)/(l)(l-l)`

B

`(YA)/(l)(l-l)^2`

C

`1/2(YA)/(l)(l-l')^2 `

D

`(YA)/(l)(l-l)^2`

Text Solution

Verified by Experts

The correct Answer is:
C
`Y = (F//A)/((Deltal)/(l))`
`therefore F = (YA)/(l) * Delta l = k * Deltal`
Force `prop` extension
If the extension is x , work done in extending by dx
dW = kx dx `" " therefore W = (1)/(2) k * x^(2)`
If x is l' - l , W = `(1)/(2) k (l' -l)^(2)`
i.e. work done is `(1)/(2) (YA)/(l) (l-l')^(2)`
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