Is the least count constant for Vernier scale or variables?

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Homework Help Overview

The discussion revolves around the concept of least count in Vernier scales, questioning whether it remains constant or varies based on measurements. Participants explore the implications of different main scale and Vernier scale readings.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants attempt to understand the relationship between main scale and Vernier scale readings in determining least count. Questions arise regarding the consistency of least count across different measurements and the design of Vernier scales.

Discussion Status

Some participants provide insights into the fixed nature of least count for specific Vernier scales, while others express confusion over differing least counts from similar scales. The conversation reflects an exploration of these concepts without reaching a consensus.

Contextual Notes

There is mention of specific measurements and least count values, but the discussion highlights potential misunderstandings regarding the application of these values across different scenarios. The original poster's examples seem to suggest variability that some participants challenge.

Medicalboy
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Homework Statement


Is the least count constant for Vernier scale like 0.1 mm or variables?

2. The attempt at a solution

If the main scale readings are 10 mm and the vernier scale readings are 9 mm, the least count is MSD/VSD = 9/10 = 0.9 So the least count is 0.1 mm for every count in the vernier scale
again if MSD is 50 mm and VSD is 49 mm, the least count is MSD/VSD = 0.98 So the least count is 0.2 for every count in the vernier scale
 
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The least count stays fixed for a particular vernier, they are the little steps the vernier can take with measurements. Your examples have one vernier with a 0.01 mm least count and the other with an 0.02 mm least count (note the extra 0 you omitted). This will stay the same for all measurements with the verniers. It does not change, that is the way the vernier is designed. The small scale divisions on the vernier scale each represents these least count values like for the 0.02 mm least count one the divisions on the vernier scale will be 0.02 mm, next division 0.04 mm, then 0.06 mm, 0.08 mm then 0.10 mm, that is the vernier division with a 1 digit next to it and so forth.
 
andrevdh said:
The least count stays fixed for a particular vernier, they are the little steps the vernier can take with measurements. Your examples have one vernier with a 0.01 mm least count and the other with an 0.02 mm least count (note the extra 0 you omitted). This will stay the same for all measurements with the verniers. It does not change, that is the way the vernier is designed. The small scale divisions on the vernier scale each represents these least count values like for the 0.02 mm least count one the divisions on the vernier scale will be 0.02 mm, next division 0.04 mm, then 0.06 mm, 0.08 mm then 0.10 mm, that is the vernier division with a 1 digit next to it and so forth.
As you said above 'The least count stays fixed for a particular Vernier'.
When the main scale division is 9mm and the vernier scale division is 10 mm, we get the least count 0.01 mm, on the other hand, for the same scale, when the main scale division is 49 mm and the vernier scale division is 50 mm, then we get the least count 0.02 mm.
So why do we get different least counts for the same vernier scale? Could you explain it, please?
 
Those are 2 different cases, they do not apply to the same vernier, that is to my knowledge you find only one vernier scale on a particular caliper.
 
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