An iron rod of length `50cm` is joined at an end to an aluminium rod of length `100cm` . All measurements 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 aluminium are `12xx10^(-6)//^(@)C` and `24xx10^(-6)//^(@)C` respectively.

An iron rod of length `50cm` is joined at an end to an aluminium rod o

1.	An iron rod of length `50cm` is joined at an end to an aluminium rod of length `100cm` . All measurements 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 aluminium are `12xx10^(-6)//^(@)C` and `24xx10^(-6)//^(@)C` respectively.
Answer» `(l_(i))_(100)=(l_(i))_(0)[1+alpha_(i)(theta-theta_(0)]` `=50[1+12xx10^(-6)(100-20)]` `=50.048cm` `(l_(a))_(100)=(l_(a)_(0)[1+alpha_(a)(theta-theta_(0)]` `=100[1+24xx10^(-6)(100-20)]` `=100.192cm` Total length at `100^(@)C` `=50.048+100.192=150.24cm` Total length at `20^(@)` `=50+100=150cm` Let average coefficient of linear expansion be `alpha` `150.24=150[1+alpha(100-20)]` `alpha=2xx10^(-5)//^(@)C` .

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