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).

A steel tape 1 m long is correctly cabibrated for a temperature of 27.

1.	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).
Answer» Solution :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`.