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  • A steel tape 1m long is correctly calibrated for a temperature of 27.0 degree 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 degree C.

Q. 11.6 A steel tape 1m long is correctly calibrated for a temperature of 27.0^{\circ}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^{\circ}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^{\circ}C\; ? Coefficient of linear expansion of steel =1.20\times 10^{-5}K^{-1}.

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At 27 oC the 63 cm (l1) mark on the steel tape would be measuring exactly 63 cm as the tape is calibrated at 27 oC

Coefficient of linear expansion of steel =1.20\times 10^{-5}K^{-1}.

Actual length when the scale is giving a reading of 63 cm on at 45 oC is l2

\\l_{2}=l_{1}(1+\alpha \Delta T)\\ =63\times (1+1.20\times 10^{-5}\times (45-27))\\ =63.013608cm

The actual length of the steel rod on a day when the temperature is 45 oC is 63.013608 cm.

Length of the same steel rod on a day when the temperature is 63 cm. 

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