Vernier Calipers

As stated in NCERT Class 11, Chapter 2 (Units and Measurements), the least count of a vernier calipers is the smallest length it can reliably measure, and it equals the difference between one main scale division (MSD) and one vernier scale division (VSD). The vernier scale is deliberately designed so that $n$ vernier divisions span $(n-1)$ main scale divisions, which makes each vernier division slightly shorter than a main scale division. Here 10 VSD coincide with 9 MSD, so one VSD $=\frac{9}{10}$ MSD $=0.9$ mm, taking 1 MSD $=1$ mm. The least count is therefore $1\text{ MSD}-1\text{ VSD}=1-0.9=0.1$ mm. Equivalently, least count $=\frac{\text{value of 1 MSD}}{\text{number of vernier divisions}}=\frac{1}{10}=0.1$ mm. The value 0.9 mm is wrong because it reports the length of one vernier division itself rather than the difference. The value 1.0 mm is wrong because it merely quotes the main scale division, ignoring the vernier refinement. The value 0.01 mm is wrong because it corresponds to a screw gauge, not a vernier of 10 divisions. The coincidence design matters because when a particular vernier mark lines up with a main scale mark, the fractional part of the reading equals that mark number times the least count, allowing sub-division precision without estimation by eye. A magnitude check confirms that a 10-division vernier on a millimetre scale resolves to one-tenth of a millimetre, exactly 0.1 mm, which is ten times finer than the bare main scale.