A `30.0 cm` long metal rod expands by `0.0650 cm` when its temperature is raised from `0^(@)C` to `100^(@)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^(@)C` to `100^(@)C`. the length of the longer portion of the composite bar in cm at `0^(@)C` is

Options

A. `23 cm`
B. `16 cm`
C. `18 cm`
D. `20 cm`

Answer

A

Explanation

Using `alpha = (Delta L)/(L_(0)*Delta T)`
`alpha_(1) = (0.0650)/(30xx100),alpha_(2) = (0.0350)/(30xx100)`
`L_(01) * alpha_(1) * Delta T + L_(02)*alpha_(2)*Delta T = 0.0580`
and `L_(01)+L_(02) = 30`
Solving `L_(01)=23 cm`.