Two rods of different materials having coefficients of linear expansion α$$1$$,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$$2=2$$:$$3$$, the thermal stresses developed in the two rods are equally provided, $$Y1$$:$$Y2$$ is equal to

Question

Two rods of different materials having coefficients of linear expansion α$$1$$,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$$2=2$$:$$3$$, the thermal stresses developed in the two rods are equally provided, $$Y1$$:$$Y2$$ is equal to

Infinity Learn · Accepted Answer

Thermal stress $$=Y$$αΔθIf thermal stress and rise in temperature are equal, then Y∝$$1$$α⇒$$Y1Y2=$$α$$2$$α$$1=32$$

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