Question

In a vernier calipers , one main scale division is $x\text{cm}$ and $n$ divisions of the vernier scale coincide with $(n-1)$ divisions of main scale. The least count (in $\text{cm}$) of the caliper is:

• A. $\left(\frac{n-1}{n}\right)$
• B. $\frac{nx}{(n-1)}$
• C. $\frac{x}{n}$
• D. $\frac{x}{x-1}$

Answer 1

The correct option is C $\frac{x}{n}$

$MSD$ = Main scale divisions
$VSD$ = Vernier scale divisions
From the data given in the question,
$1MSD=x\text{cm}$ and
$n$ divisions of $VSD$ coincides with $(n-1)$ divisions of $MSD$.
$\Rightarrow nVSD=(n-1)MSD$
$\Rightarrow 1VSD=\left(\frac{n-1}{n}\right)MSD$
$\Rightarrow 1VSD=\left(\frac{n-1}{n}\right)\times x\text{cm}$
Vernier constant$\left(VC\right)$ or Least count$\left(LC\right)=1MSD-1VSD=x-\left(\frac{n-1}{n}\right)x=\frac{x}{n}\text{cm}$
Hence, option (c) is the correct answer.