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Question

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

A
50.24 cm, 10×106/C
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B
160.24 cm, 120×106/C
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C
150.24 cm, 20×106/C
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D
250.5 cm, 25×106/C
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Solution

The correct option is C 150.24 cm, 20×106/C
The length of the iron rod at 100C is
The length of the aluminum rod at 100C isl2=(100 cm)[1+(24×106/C)(100C20C)]=100.192 cmThe length of composite system at 100C is50.048+100.192=150.24 cm
The length of the composite system at 20C is 150 cm. So, the average coefficient of linear expansion of the composite rod is
α=0.24 cm150 cm×(100C20C)=20×106/C

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