On a fairly cool rainy day when the temperature is 20°C; the length of a steel railroad track is 20m. What will be its length on a hot a dry day when the temperature is 40°C? [coefficient of linear expansion of steel = 11 x 10^-6K‾¹]

A. 20.013m
B. 20.009m
C. 20.004m
D. 20.002m

Correct Answer:

Option C – 20.004m

Explanation

The increase in length of the steel rail is given by
= α 10
= 11 x 10^-6 x 20 x (40 -20)
= 11 x 10^-6 x 20 x 20
= 4.4 x 10^-3
∴ Final length will be original length plus increase in length
= 20 + 4.4 x 10^-3
= 20 + 0.0044
= 20.0044m