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# 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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a
20 cm
b
10 cm
c
15 cm
d
18 cm
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detailed solution

Correct option is B

ΔL=L0αΔθRod⁡A:0.075=20×αA×100⇒αA=752×10−6/∘Crod⁡B:0.045=20×αB×100⇒αB=452×10−6/∘CFor composite rod: x cm of A and (20 - x) cm of B, we have0.060=xαA×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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The coefficient of linear expansion of brass and steel are ${\mathrm{\alpha }}_{1}$ and ${\alpha }_{2}$. If we take a brass rod of length ${l}_{1}$ and steel rod of length ${l}_{\mathit{2}}$ at 0oC, their difference in length $\left({l}_{2}-{l}_{1}\right)$will remain the same at all temperatures if

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