Question

The main scale of a vernier callipers has n divisions/cm. n divisions of the vernier scale coincide with (n - 1) divisions of main scale. The least count of the vernier callipers is,

• A. $\frac{1}{\left(n +1\right)\left(n -1\right)}cm$
• B. $\frac{1}{n}cm$
• C. $\frac{1}{n^{2}}cm$
• D. $\frac{1}{n\left(n + 1\right)}cm$

Answer 1

Answer: (C)

$\frac{1}{n^{2}}cm$

Answer 2

$n(VSD) = (n - 1)MSD$ $\Rightarrow 1\,VSD = \frac{(n - 1)}{n} MSD$ Least count $= 1 \,MSD - 1 \,VSD = [ 1 - \frac{(n -1)}{n}]$ $MSD = \frac{1}{n} MSD$ $= \frac{1}{n} (\frac{1}{n}) cm$ $= \frac{1}{n^2} cm$