11.6 A steel tape 1m 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 = 1.20 × 10–5 K–1 .

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    Answered by

    Payal Gupta | Contributor-Level 10

    4 months ago

    11.6 Length of the steel tape, l = 1 m = 100 cm, At temperature T = 27 ° C

    Coefficient of linear expansion of steel α = 1.2 ×10-5 / K

    Let l1=63cm be the length of the steel rod at temperature T1 = 45.0 °C and

    l2 be the length of the steel rod and l’ be the length of the steel tape at 45.0 °C

    We have l’ = l + αl (T1-T) = 100 + 1.2 ×10-5×100×  (45-27) = 100.0216 cm

    l2 can be calculated as l2 = l'l×63 = 63.0136 cm

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