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 `27^(@)C` is `100cm` i.e., `L=100cm and T = 27^(@)C`
The length of steel tape at `45^(@)C` is `L ' = L+Delta L = L + alpha L Delta T`
`=100+(1.20xx10^(-5))xx100xx(45^(@)-27^(@))=100.0216cm`
Length of `1cm` mark at `27^(@)C` on this scale, at `45^(@)C` =`100.0216//100cm`
lenght of `63cm` measured by this tape at `45^(@)C` will be = `(100.0216)/(100)xx63 =63.0136 cm`
Lenght of the same steel rod on a day when the temperature is `27^(@)=63xx1 = 63cm`.