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A steel tape 1 m long is correctly cabib...

A steel tape 1 m long is correctly cabibrated for a temperature of `27.0^(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^(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^(0)C` ? Co-efficient of linear expansion of steel `=1.20xx10^(-5)""^(@)C^(-1)`.

Text Solution

Verified by Experts

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