Two rods of different materials having coefficients of thermal expansion α$$1$$,α$$2$$ and Young’s modulli $$Y1$$, $$Y2$$ 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 the rods. If α$$1$$:α$$2$$ $$=$$ $$2$$ : $$3$$, 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 thermal expansion α$$1$$,α$$2$$  and Young’s modulli $$Y1$$, $$Y2$$ 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 the rods. If  α$$1$$:α$$2$$  $$=$$ $$2$$ : $$3$$, the thermal stresses developed in the two rods are equal provided $$Y1$$ : $$Y2$$ is equal to :

Infinity Learn · Accepted Answer

Thermal stress  $$Y1$$α$$1$$Δ$$t=Y2$$α$$2$$Δ$$tY1Y2=$$α$$2$$α$$1=32$$

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