Does Temperature Affect the Accuracy of a Steel Metre Scale?

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SUMMARY

The discussion centers on the impact of temperature on the accuracy of a steel metre scale, specifically calibrated at 20 degrees Celsius. When used at 10 degrees Celsius, the scale's distance between the 50 cm and 51 cm marks is calculated using the formula L = Lo(1 + αθ), where α is the coefficient of linear expansion (1.1 x 10-5 C-1) and θ is the temperature change (-10 degrees). The calculated distance is 1.00011 cm, which contradicts the expectation that the distance should decrease due to contraction, leading to confusion among participants regarding the interpretation of the problem.

PREREQUISITES
  • Understanding of linear expansion and the coefficient of linear expansion.
  • Familiarity with basic physics equations related to thermal expansion.
  • Knowledge of temperature scales and their conversions.
  • Ability to interpret physics problems and equations from textbooks.
NEXT STEPS
  • Study the principles of thermal expansion in solids, focusing on steel.
  • Review the derivation and application of the linear expansion formula L = Lo(1 + αθ).
  • Examine examples of temperature effects on measurement accuracy in physics.
  • Explore the textbook "Concepts of Physics (Part 2)" by H.C. Verma for further context and problems.
USEFUL FOR

Students studying physics, particularly those focusing on thermal expansion and measurement accuracy, as well as educators seeking to clarify concepts related to temperature effects on materials.

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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 + [tex]\alpha\theta[/tex])
[tex]\theta[/tex] = -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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