Question

# An iron rod of length 50 cm is joined at an end to an aluminum rod of length 100cm. All measurement refer to 20∘C. Find the length of the composite system at 100∘C and its average coefficient of linear expansion. The coefficient of linear expansion of iron and aluminum are 12×10−6/∘C and 24×10−6/∘C respectively.

A
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B
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C
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D
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Solution

## The correct option is C The length of the iron rod at 100∘C is The length of the aluminum rod at 100∘C isl2=(100 cm)[1+(24×10−6/∘C)(100∘C−20∘C)]=100.192 cmThe length of composite system at 100∘C is50.048+100.192=150.24 cm The length of the composite system at 20∘C is 150 cm. So, the average coefficient of linear expansion of the composite rod is α=0.24 cm150 cm×(100∘C−20∘C)=20×10−6/∘C

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