Let length LS of measuring steel scale at 0°C = 100 cm.
Length LZ of zinc rod at 0°C = 100 cm.
actual length of steel scale at 100°C = LS(1 + αS × ΔT) = 100(1+1.2×10-5×100) = 100.12 cm
actual length of zinc rod at 100°C = LZ(1 + αZ × ΔT) = 100(1+2.6×10-5×100) = 100.26 cm
where αS and αZ are linear thermal expansion coefficient of steel and zinc respectively.
Zinc rod has expanded more than steel scale.
If the expanded zinc rod is measured using expanded steel rod, then the ratio is = 100.26/100.12 = 1.001398
Hence 0.001398 part of zinc rod is measured again by same expanded steel scale.
Then the measured length of remaining part = 100.12×0.001398 = 0.14 cm
Hence the measured value by expanded steel scale = 100+0.14 = 100.14 cm