A rod of length $$20$$ cm is made of metal. It expands by $$0.075cm$$ when its temperature is raised from $$0$$°C to $$100$$°C. 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

Question

Infinity Learn · Accepted Answer

Rod A : $$0.075$$ $$=$$ $$20$$ x A x $$100$$  rod B : $$0.045$$ $$=$$ $$20$$ x B x $$100$$  For composite rod : x cm of A and (20$$ – $$x) cm of B we $$have0.060$$ $$=$$ x A x $$100$$ $$+$$ (20$$ – $$x) B x $$100$$          On solving we get x $$=$$ $$10$$ cm

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