Does Temperature Affect the Accuracy of a Steel Metre Scale?

AI Thread Summary
Temperature affects the accuracy of a steel metre scale, as it is calibrated at 20 degrees Celsius. When used at 10 degrees Celsius, the scale's contraction should theoretically reduce the distance between marks. However, calculations show the distance between the 50 cm and 51 cm marks to be 1.00011 cm, which contradicts expectations. This discrepancy arises from the interpretation of the problem, suggesting that the scale's calibration accounts for temperature effects. The discussion highlights the importance of understanding thermal expansion in practical applications.
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Homework Statement


A metre scale made of steel is calibrated at 20 degrees Celsius to give correct reading. Find the distance between 50cm mark and 51cm mark if the scale is used at 10 degrees Celsius. Coefficient of linear expansion of steel is 1.1 x 10-5 C-1


Homework Equations





The Attempt at a Solution



L=Lo(1 + \alpha\theta)
\theta = -10
Lo = 1cm
on solving, L = 0.99989cm which is the distance between 50 and 51 cm mark.

The answer is 1.00011cm.
I don't see any logic behind this answer. As the scale is cooled, it contracts. Hence the distance between any two consecutive marks should decrease (<1cm). But the answer is contradicting.

Help please
 
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I agree with your answer. The problem statement is slightly ambiguous, but I would interpret it exactly as you have.

(What book is this from?)
 
It is from Concepts of Physics (Part 2) by H.C. Verma.
There are no wrong answers given in this book (as per my experience)
 

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