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.

Options

A. `36 xx 10^(-6 //@)C`
B. `12 xx 10^(-6 //@)C`
C. `20 xx 10^(-6 //@)C`
D. `48 xx 10^(-6 //@)C`

Answer

C

Explanation

`Deltal_(1)+Deltal_(2)=Delta_(l),l_(1)alpha_(1)Delta_(t)+Delta_(2)alpha_(2)Deltat=(l_(1)+l_(2))alpha_(ave)Deltat`
`alpha_(avg) = (alpha_(1)l_(1) + alpha_(2)l_(2))/(l_(1) + l_(2))`