A steel tape I 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°C. Coefficient of linear expansion of steel = 1.20 x ${10}^{-5}$/K. What is the actual length of the steel rod on that day?

detailed solution

Correct option is A

The steel tape gives correct reading only at the temperature 27°C at which it has been calibrated. At any other temperature 45°C the scale will expand and give less reading than the true value.Hence length of the steel rod at 27°C, i.e., L = 63 cmLet ∆L be the increase in the length of the steel tape when temperature rises from 27°C to 45°C, i.e.,∆T = 45°C-27°C =18°C = 18KClearly, ∆L = α L∆T= (1.20 x 10-5/K) x (63 cm) x l8 K = 0.0136 cmActual length of the rod at 45°C = 63 cm + 0.0136 cm = 63.0136 cm