Question

Question 11. 6.  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 = 1.20 x 10-1K-1.​

Answer 1

Hey mate,....

Here,

Length of steel tape at 27°C ( Lo) = 1m or 100 cm

temperature Change( ∆T) = 45° - 27° = 18°C

Coefficient of linear expansion of steel ( a) = 1.2 × 10^-5 /°C

Length of steel tape at 45°C ,

Use expansion formula,

L = Lo( 1 + a∆T)

= 100( 1 + 1.2 × 10^-5 × 18)

= 100 (1.000216)

= 100.0216 cm

So, length of 1 cm at 45°C = 100.0216/100 = 1.000216 cm

So, length of 63cm at 45°C = 1.000216 × 63 = 63.0136 cm

Hope it will help you.

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