A steel tape 1 m 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 =1.20xx10^(-5)K^(-1).

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

1.	A steel tape 1 m 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 =1.20xx10^(-5)K^(-1).
Answer» SOLUTION :Length of steel tape at `27^(@)C`, `l_(0)=1m=100cm` `alpha=1.2xx10^(-5)K^(-1)` Length of steel tape `45^(@)C`, `l.=l_(0)+alphal_(0)Deltatheta` `=100+1.2xx10^(-5)xx100xx(45-27)` `=100+1.2xx10^(-3)xx18` `=100+0.0216` `:.l.=100.0216cm` Actual length of steel tape at `45^(@)C`, `l_(45)=(l.)/(l_(0))XXL"where "l=63." cm"` `=(100.0216xx63)/(100)""l_(0)=100" cm"` `=63.0136" cm"` No. of least SIGNIFICANT figures is 3 in `63.0` cm. HENCE actual length upto 3 significant figures is `63.0` cm. `:.` At `27^(@)C` temperature, 1 cm on measure tape is catually 1 cm. `:.` Length of tape at `27^(@)C=63.0xx1` `=63.0` cm