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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 proportional to`(Delta T)/(Y)`

D

independent of L

Text Solution

Verified by Experts

The correct Answer is:
D
As stain `=(Delta L ) /( L)`
Also `Delta L = alpha L apha Delta T therefore (Delta L)/(L ) = alpha Delta T `
As ` Y=("Stress ")/("Strain") therefore "Stress "=Y xx "Straon " = Y alpha Delta T `
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