A `30.0 cm` long metal rod expands by `0.0650 cm` when its temperature is raised from `0^(circ) C` to `100^(circ) C`. A second rod of different metal and of the same length expands by `0.0350 cm` for the same rise in temperature, A third composite rod, also `30.0 cm` long, is made up of pieces of each of the above metals placed end to end and expands by `0.0580 cm` when temperature is increased from `0^(circ) C` to `100^(circ) C`. Find the length (in `cm` ) of the smaller portion of the composite rod at `0^(circ) C`.

Answer

7