A steel tape 1m 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 `63.0cm` 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 `=1.20xx10^(-5)K^(-1)`

Explanation

Length of steell tape at `27^(@)C` is `100cm` i.e. `L=100cm` and `T=27^(@)C`
The length of steel tape at `45^(@)C` is `L^(1)=L+DeltaL`
`=L+alphaLDeltaT`
`=100+(1.20xx10^(-5))xx100xx(45^(@)-27)`
`=100.0216cm`
Length of 1cm mark at `27^(@)C` on this scale, at `45^(@)C`
`=100.216//100cm`
Length of 63cm measured by this tape at `45^(@)C` will be
`=(100.0216)/(100)xx63=63.0136cm`
Length of the same steel rod on a day when the temperature is `27^(@)C=63xx1=63cm`