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VSD - Vernier scale divisions. MSD - Main scale divisions.
Given that 20 VSD = 19 MSD
Then 1 VSD = (19)/(20) MSD= 0.95 MSD.
Least count of Vernier calipers, LC = 1 MSD -1 VSD
= 1 MSD - 0.95 MSD = 0.05 MSD.
As 1 MSD = 2mm,
Least count, LC = 0.05 x 2 mm = 0.1 mm.