Question

The main scale of Vernier callipers have $n$ equal divisions per cm. $n$ divisions of main scale is equal to $(n+2)$ divisions of Vernier scale. The least count of the Vernier callipers is

• A. $\frac{1\text{cm}}{n(n+2)}$
• B. $\frac{2\text{cm}}{n^2}$
• C. $\frac{2\text{cm}}{n(n+2)}$
• D. $\frac{4\text{cm}}{n^2(n+2{)}^2}$

Answer 1

The correct option is C $\frac{2\text{cm}}{n(n+2)}$

Answer (1)
Least count $\left(\text{LC}\right)=1\text{MSD}-1\text{VSD}$
$\Rightarrow \text{LC}=\frac{1}{n}\text{cm}-\left(\frac{n}{n+2}\right)\frac{1}{n}\text{cm}$
$=\frac{1}{n}\text{cm}\left(\frac{n+2-n}{n+2}\right)$
$=\frac{2\text{cm}}{n(n+2)}$