a metal rod A of 25 cm length expands by 0.050 cm when its temperature is rasied from 0 deg to 100 deg. another rod B of a different metal of length 40 cm expands by 0.040 cm for the same rise in temp. A third rod C of 50 cm length is made up of pieces of rods A and B placed end to end expands by 0.03 cm on heating from 0 deg to 50 deg. Find the lengths of each portion of the composite rod.
For rod A alpha_A = .05/25/100 = 2e-5
For rod B alpha_B = .04/40/100 = 1e-5
If composite rod is x cm A and 50-x cm B then
x*50*2e-5 + (50-x)*50*1e-5 = 0.03
x+50 = 60
x = 10
so composite rod is 10 cm A and 40 cm B