A steel tape Im 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 xx 10^(-5) K^(-1)`.

Explanation

Length of the steel tape at `27^(@)C` is 100 cm.
i.e. L = 100 cm and T = `27^(@)C`.
The length of steel tape at `45^(@)C` is
`L=L+DeltaL=L+alphaLDeltaT`
= `100+(1.20xx10^(-5))xx100xx(45^(0)-27^(0))`
= 100.0216 cm
The length of 1 cm mark at `27^(@)C` on this scale, at `45^(@)C` = 100.0216/100 cm.
Length of 63 cm measured by this tape at `45^(@)C` will
be = `(100.0216)/100xx63=63.0136cm`
Length of the same steel rod on a day when the temperature is `27^(@)C=63xx1=63cm`.