A steel tape 1m long is correctly calibrated for a temperature of `27^(@)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 acutual 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) .^(@)C^(-1)`.

Explanation

Length of tape at `27^@C = l = 100 cm`
Length of tape at `45^@C = l.=l+Delta l`
` = l+ alpha l Delta T = 100 + (1.20 xx 10^(-5) ) 100 (45 - 27) = 100.0216 cm `
Length of 1 cm mark on this scale at `45^@C= (100.0216)/(100)`
Length of 63 cm mark on this scale at `45^@C`
` = (100.0216)/(100 ) xx 63 = 63.0136 cm `
The steel tape is calibrated for a temperature of `27^@C` . Therefore, length of steel rod at `27^@C = 63 cm` .