Measuring Instruments And Least Count
A vernier scale has ten divisions that exactly coincide with nine divisions of a main scale whose smallest division equals one millimetre; what is its least count?
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About This Question
- Subject
- physics
- Chapter
- physics and measurement
- Topic
- measuring instruments and least count
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
0.01 cm
The least count of a vernier caliper is the smallest length it can resolve, found from the difference between one main-scale division and one vernier-scale division. Since ten vernier divisions span the same length as nine main-scale divisions, one vernier division equals 9/10 of a main-scale division. With the smallest main-scale division being 1 mm, one vernier division measures 0.9 mm. The least count is therefore 1 MSD minus 1 VSD = 1 mm - 0.9 mm = 0.1 mm, which equals 0.01 cm. The choice 0.1 cm equals one whole millimetre, the main-scale division itself, and ignores the vernier refinement. The choice 0.001 cm would require a hundred vernier divisions matching ninety-nine main divisions, which is not the case here. The choice 1 mm simply restates the main-scale division and is not a least count at all. This is precisely the standard formula least count = value of one main-scale division divided by the number of vernier divisions. As a check, dividing 1 mm by 10 vernier divisions gives 0.1 mm, confirming 0.01 cm.
This easy difficulty physics question is from the chapter physics and measurement, covering the topic of measuring instruments and least count. It appeared in the 2025 exam.
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