A metal rod is fixed rigidly at two ends so as to prevent its thermal expansion. If L, α and Y respectively denote the length of the rod, coefficient of linear thermal expansion and Young's modulus of its material, then for an increase in temperature of the rod by ∆T, the longitudinal stress developed in the rod is [AMU $$2014$$]

Question

A metal rod is fixed rigidly at two ends so as to prevent its thermal expansion. If L, α and Y respectively denote the length of the rod, coefficient of linear thermal expansion and Young's modulus of its material, then for an increase in temperature of the rod by ∆T, the longitudinal stress developed in the rod is [AMU $$2014$$]

Infinity Learn · Accepted Answer

Strain $$=$$ α·∆T  ⇒  Stress $$=$$α Y∆Twhere, L $$=$$ length of the rod,            α $$=$$ coefficient of linear thermal expansionand      Y $$=$$ Young's modulus of its material.So, the longitudinal stress developed in the rod is independent of L

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