Question

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.

Answer 1

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

Answer 2

Answer:

the actual length is 63.013608cm. the length of the same steel rod on a day when the temp is 27°C is 63cm.

Explanation:

refer the attachment.

hope this helps :)