A steel tape 1m long is correctly calibrated for a temperature of `27^(@)C`. The length of a steel rod measured by this tape is found to be `63.0cm` on a hot day when the temperature is `45.0^(@)C`. What is the acutual 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 ` = 1.20xx10^(-5) .^(@)C^(-1)`.

Explanation

Length of the steel tape at temperature` T = 27^(@)C`, l = 1 m = 100 cm
Coefficient of linear expansion of steel, `α = 1.20 x× 10^(–5) K^(–1)`
Let `l_(2)` be the actual length of the steel rod and l‘ be the length of the steel tape at `45^(@)C`.
`l'=l+al(T_(1)-T)`
`:.l'=100+1.20xx10^(-5)xx100(45-27)`
= 100.0216 cm
Hence, the actual length of the steel rod measured by the steel tape at 45°C can be calculated as:
`l^(2)=(100.0216)/(100)xx63=63.0136 cm`
Therefore, the actual length of the rod at `45.0^(@)C` is 63.0136 cm. Its length at `27.0^(@)C` is 63.0 cm.