Question

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

• A. $\frac{a}{2n+1}$.
• B. $\frac{a}{n+1}$.
• C. $\frac{a}{3n+1}$.
• D. $\frac{a}{4n+1}$.

Answer 1

Answer: (B)

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

$\begin{array}{cc}& nMSD=(n+1)VSD⟶\left(i\right),\\ & 1MSD=a\text{unit}⟶\left(ii\right)\\ & \Rightarrow \text{no units}=(n+1)\text{VSD}\\ & \Rightarrow 1VSD=\left(\frac{na}{n+1}\right)units\end{array}$

$\begin{array}{cc}LC& =\mathrm{1MSD}-1VSD\\ & =a-\frac{na}{n+1}\\ & =\frac{a}{n+1}\text{unils}\end{array}$