Question

The least count of a Vernier calliper is $0.001$cm. One cm on the main scale is divided into $20$ divisions. How many divisions are there on the Vernier scale?

• A. $40$
• B. $30$
• C. $20$
• D. $50$

Answer 1

Answer: (D)

$50$

$\begin{array}{c}L\cdot C=0.001cm\\ 1MSD=\frac{1}{20}cm=\\ L\cdot C=1MSD-1VSD\\ \Rightarrow 0.001=0.05-1VSD\\ \Rightarrow 1VSD=0.049\end{array}$

$\begin{array}{c}\text{Let}\\ n\text{MSD}=m\text{VSD}\\ n\times \frac{1}{20}=m\times 0.049\\ \frac{n}{m}=\frac{50}{49}\\ (n\&m\text{are whole numbers )}\\ n=50\end{array}$