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A metal rod of length 'L' and cross-se...

A metal rod of length 'L' and cross-sectional area 'A' is heated through `'T'^(@)C` What is the force required to prevent the expansion of the rod lengthwise ?

A

`(YA alphaT)/((1-alphaT))`

B

`(YA alphaT)/((1-alphaT))`

C

`((1-alphaT))/(YA alphat)`

D

`((1+alphaT))/(YA alphat)`

Text Solution

Verified by Experts

The correct Answer is:
B
`DeltaL=alphaLT.....(i)`
`Also, Y=F/A.(L(1+alphat))/(DeltaL)`
`or DeltaL=(F.L(1+alphat))/(A.Y).....(ii)`
Equating (i) and
`(FL(1+alpha t))/(AY)=alphaLT`
`therefore F=(AYalphaT)/((1+alphat))`
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Knowledge Check

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