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.

Explanation

`(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` .