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2. Rod A, which is 30 cm long, expands by 0.045 cm when heated from 0°C to 100°C. Rod B, also 30 cm long expands by 0.075 cm for the same change in temperature. A third Rod C, also 30 cm long is made up of the materials of rod A and B, connected end to end. It expands by 0.065 cm when heated from 0°C to 100°C. Calculate the initial lengths of rods A and B in rod C.
Let X be the length of material of rod A and 30-X be the length of material of rod B. We have
0.065 = (0.045/30)*X + [30-X]*(0.075/30) = 0.0015*X + 0.075 - 0.0025*X or
0.001*X = 0.075 - 0.065 = 0.010 or X = 10 cm. So initial length of rod A was 10 cm and rod B was 20 cm