Two rods of different materials and identical cross sectional area, are joined face to face at one end and their free ends are fixed to the rigid walls. If the temperature of the surroundings is increased by $$30$$°C, the magnitude of the displacement of the joint of the rod is (length$$ of rods $$l1=l2=1unit$$, ratio of their young's moduli, $$Y1/Y2=2$$, coefficients of linear expansion are α$$1$$ and α$$2)

Question

Infinity Learn · Accepted Answer

$$Y1($$ Strain $$)1=Y2($$ Strain $$)2Y1a1l$$Δ$$T1$$−$$xl=Y2a2l$$Δ$$T2+xl$$ Displacement of the rod $$x=Y2a2$$−$$Y1a1Y1+Y2$$×l×ΔT

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