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A metal rod if fixed rigidly at two ends...

A metal rod if fixed rigidly at two ends so as to prevent its hermalexpension. If L,`alpha` Y respectively denote the length of the rod , coefficeent of linear thermal expension and Young's modulus of its material, then for an increase in temperature of the rod by `Delts`T, the longitudinal stress developed in the rod is

A

inversely proportional to `alpha`

B

inversely proportional to Y

C

directly proportinal to `Delta`T/Y

D

independent of L

Text Solution

Verified by Experts

The correct Answer is:
C
Srrain `=alpha.DeltaT rArr "Stress"YpropDeltaT`
where ,L= length of the rod
`alpha=` coefficient of linear thermal expansion and Y = Young's modulus of its material
So, the longitudinal stress developed in the rod is directily proportional to `(DeltaT)/(Y).`
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