Q: In a vernier callipers N divisions of vernier scale coincide with N –1 divisions of main scale (in which length of one division is 1 mm). The least count of the instrument should be

(a) N

(b) N – 1

(c) 1/10N

(d) 1/((N – 1))

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Ans: (c)

Sol: N VSD = (N-1) MSD

$\displaystyle 1 VSD = \frac{N-1}{N} MSD$

Least Count = 1 MSD – 1 VSD

$\displaystyle L.C = 1 MSD – \frac{N-1}{N}MSD = \frac{1}{N} MSD$

$\displaystyle L.C = \frac{1}{N} MSD = \frac{1}{N}\times 0.1 cm $

$\displaystyle L.C = \frac{1}{10 N}$