Two rods of different materials having coefficients of linear expansion α$$1$$ and α$$2$$ and Young's moduli, $$Y1$$ and $$Y2$$, respectively, are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If α$$1/$$α$$2=2/3$$, then the thermal stresses developed in the two rods are equal, provided $$Y1/Y2$$ is equal to

Question

Two rods of different materials having coefficients of linear expansion α$$1$$ and α$$2$$ and Young's moduli, $$Y1$$ and $$Y2$$, respectively, are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If α$$1/$$α$$2=2/3$$, then the thermal stresses developed in the two rods are equal, provided $$Y1/Y2$$ is equal to

Infinity Learn · Accepted Answer

Thermal stress $$=Y$$αtIn the given problem,    Yα$$=$$ constant $$Y1Y2=$$α$$2$$α$$1=32$$

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