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Question

A iron rod of length 50 cm is joined at an end to an aluminum rod of length 100 cm. All measurements refer to 20C. The coefficients of linear expansion of iron and aluminum are 12×106/C and 24×106/C respectively. The average coefficient of composite system is

A
36×106/C
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B
12×106/C
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C
20×106/C
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D
48×106/C
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Solution

The correct option is C 20×106/C
Initially (at 20C) length of composite system L = 50 + 100 = 150 cm
Length of iron rod at 100C =50[1+12×106×(10020)]=50.048cm
Length of aluminum rod at 100C =100[1+24×106×(10020)]=100.192cm
Finally (at 100C) length of composite system L' = 50.048+100.192=150.24cm
Change in length of the composite system ΔL = L' - L = 150.24 -150 = 0.24 cm
Average coefficient of expansion at 100C α=ΔLL×ΔT= 0.24150×(10020) = 20×106/C

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