A metal rod of 30 cm length expands by 0.075 cm when its temperature is raised from `0^@C` to `100^@C`. Another rod of a different metal of length 45 cm expands by 0.045 cm for the same rise in temperature. A composite rod C made by joining A and B end to end expands by 0.040 cm when its length is 45 cm and it is heated from `0^@C` to `50^@C`. Find the length of each portion of the composite rod.

Explanation

`Deltal=lalphaDeltaT` or `0.075=30xxalpha_(A)xx100`
or `alpha_(A)=25xx10^-6^@C^-1`
and `0.045=45xxalpha_(A)xx100`
or `alpha_(B)=10xx10^-6^@C^-1`
let `l_1` and `l_2` be the lengths of the two section of C.
Then `l_1+l_2=45` and
`0.04=l_1xx25xx10^-6xx50+l_2xx10xx10^-6xx50`
Solving `l_1=23.3cm`
`l_2=21.7cm`