Question

A steel tape 1 m long is correctly calibrated for a temperature of 27.0°C. The length of a steel rod measured by this tape is found to be 63.0 cm on a hot day when the temperature is 45.0°C. What is the actual length of the steel rod on that day? What is the length of the same steel rod on a day when the temperature is 27.0°C? Coefficient of linear expansion of steel = 1.20 x 10-5°C-1.

Answer 1

The length of the steel tape of 27°C is 100 cm

∴ L = 100 m and T = 27°C

∴ Its length at 45°C

L' = L + ΔL

= L + α x L x ΔL

= 100 + 1.2 x 10-5 x 100 x (45 - 27)

= 100.0216 cm

∴ The length of 63 cm measured by this tape at 45°C will actually be

= {100.0216}/{100} x 63 = 63.0136 cm

Length of the same steel rod shall again be 63 cm when measured by the same tape at 27°C.