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