A rod of length $$20$$ cm is made of metal. It expands by $$0.075cm$$ when its temperature is raised from $$0oC$$ to $$100oC$$. Another rod of a different metal B having the same length expands by $$0.045$$ cm for the same change in temperature. A third rod of the same length is composed of two parts, one of metal A and the other of metal B. This rod expands by $$0.060$$ cm for the same change in temperature. The portion made of metal A has the length

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Δ$$L=L0$$αΔθRod⁡A:$$0.075=20$$×αA×$$100$$⇒α$$A=752$$×$$10$$−$$6/$$∘Crod⁡B:$$0.045=20$$×αB×$$100$$⇒α$$B=452$$×$$10$$−$$6/$$∘CFor composite rod: x cm of A and (20$$ $$-$$ $$x) cm of B, we $$have0.060=x$$αA×$$100+(20$$−$$x)$$αB×$$100=x752$$×$$10$$−$$6$$×$$100+(20$$−$$x)$$×$$452$$×$$10$$−$$6$$×$$100On$$ solving, we get x $$=$$ $$10$$ cm.

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