Does Temperature Affect the Accuracy of a Steel Metre Scale?

In summary, the problem involves finding the distance between two marks on a steel metre scale at 10 degrees Celsius, given that it was calibrated at 20 degrees Celsius and has a coefficient of linear expansion of 1.1 x 10-5 C-1. The solution involves using the equation L=Lo(1 + \alpha\theta), where L is the final length, Lo is the original length, and \alpha is the coefficient of linear expansion. On solving, the distance between the two marks is 0.99989cm, which is consistent with the scale contracting as it is cooled. The given answer of 1.00011cm is contradictory to this logic.
  • #1
zorro
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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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  • #2
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?)
 
  • #3
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)
 

What is a metre scale and how is it used?

A metre scale is a measuring tool used to measure small distances up to one metre. It is typically made of metal or plastic and has markings in centimetres and millimetres. It is commonly used in science experiments and construction projects.

What is the contradiction surrounding the metre scale?

The contradiction surrounding the metre scale is related to the accuracy and precision of its measurements. While it is designed to measure up to one metre, the markings on the scale can only be as precise as the manufacturing process allows, leading to potential discrepancies in measurements.

What is the difference between accuracy and precision in measurement?

Accuracy refers to how close a measurement is to the true value, while precision refers to how close multiple measurements are to each other. A metre scale may have high accuracy if its markings are aligned with the true distance, but low precision if there are variations in the markings from one scale to another.

How can the contradiction of a metre scale be overcome?

To overcome the contradiction of a metre scale, it is important to use proper measurement techniques and to account for potential errors. This can include taking multiple measurements and calculating an average, using a more precise measuring tool for smaller distances, and understanding the limitations of the metre scale.

What other types of measuring tools can be used instead of a metre scale?

Other types of measuring tools that can be used instead of a metre scale include rulers, calipers, and micrometers. These tools are designed to measure smaller distances with higher precision and can be used to verify the accuracy of a metre scale's measurements.

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