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Units And Measurement

Question
CBSEENPH11016684

What do you mean by vernier constant? Find its value for the vernier calliper whose n divisions on vernier scale coincide with (n–1) divisions of main scale.

Solution
Vernier constant of a vernier calliper is equal to difference in the value of one main scale division and one vernier scale division. It is also equal to least count of the instrument.
Here n vernier scale divisions coincides with (n–1) main scale divisions. So, 
         n VSD = (n - 1) MSD
         1 VSD = fraction numerator straight n minus 1 over denominator straight n end fraction MSD
space space therefore Vernier constant (VC) = 1 MSD - 1 VSD
                                  space space space space space equals space 1 space MSD space minus space fraction numerator straight n minus 1 over denominator straight n end fraction MSD 
                                       = 1 over straight n MSD