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)

$n(VSD) = (n - 1)MSD$
$\Rightarrow 1\,VSD = \frac{(n - 1)}{n} MSD$
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$