Question

In a verneir calipers, $n$ divisions of its main scale match with $(n+1)$ divisions on its Vernier scale. Each divisions of the main scale is a units. Using the Vernier principle, calculate its least count.

• A. $\frac{1}{n}$
• B. $\frac{1}{n+1}$
• C. $\frac{n}{2}$
• D. $n+1$

Answer 1

Answer: (B)

$\frac{1}{n+1}$

$\begin{array}{cc}\text{Given -}nMSD& =(n+1)\text{. VSD.}\\ \text{MSD}& =\text{Main scale division}\\ \text{VS D}& =\text{Vernier scale division.}\end{array}$

$\text{Least Count}=1\text{MSD-1VSD}$

$\begin{array}{cc}\text{since}(n+1)& \text{VSD}=n\text{. MSD}\\ & \text{1VSD}=\frac{n}{n+1}.\text{MSD.}\end{array}$

$\Rightarrow \text{Least Count}=\mathrm{IMSD}-\frac{n}{n+1}\cdot MSD$

$=\frac{n+1-n}{n+1}MSD=\frac{1}{n+1}\cdot MSD$

$\begin{array}{c}\text{Since}1MSD=\text{1 unit}\\ \Rightarrow \text{Least count}=\frac{1}{n+1}\end{array}$