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Question

An iron rod of length 50 cm is joined at an end to an aluminium rod of equal length to form a system. All measurements refer to 20C. If coefficient of linear expansion of iron and aluminium are 12×106/C and 24×106/C respectively, find average coefficient of linear expansion of composite system?

A
36×106C
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B
20×106C
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C
24×106C
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D
38×106C
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Solution

The correct option is A 36×106C
Change in length of iron rod
ΔLi=αiΔT
Similarly
Change in length of aluminium rod
ΔLa=αaΔT
Change in length of system
ΔL=ΔLi+ΔLa
=(αi+αa)ΔT
average coefficient of linear expension of composite system=ΔLΔT=(αi+αa)=12×106/C+24×106/C=36×106/C

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