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

The length of the iron rod at `100^(@)C` is
`l_(1)=(50)[1+(12xx10^(-6))(100^(@)C-20^(@)C)]`
`=100.192cm`
The length of the composite system at `100^(@)C` is `50.048 cm + 100.192 cm = 150.24` cm.
he length of the composite system at `20^(@)C` is 150 cm. So, the average coefficient of linear expansion of the composite rod is
`alpha=(0.24)/(150xx(100^(@)C-20^(@)C))=20xx10^(6)//^(@)C`