Question

The length is measured using a vernier system whose main scale is $30cm$ long with $600$ divisions. If $19$ divisions of the main scale coincide with $20$ divisions of the vernier scale, then its least count is

• A. $0.25cm$
• B. $0.025cm$
• C. $2.5m$
• D. $0.0025mm$

Answer 1

Answer: (D)

$0.0025mm$

Given - A Velenier Scale with $30cm$ with $600div$.

* $19MSD=2OVSD$ MSD=main Scale div VSD = vernier scale div

We have $30cm=600MSD$

$\Rightarrow \mid 1MSD=\frac{1}{20}cm=0.05cm$ $\begin{array}{cc}\text{and}& 20VSD=19MSD\\ & \Rightarrow \mathrm{1VSD}=\frac{19}{20}\cdot \left(0.05\right)cm.\\ \text{Least count}=& \text{1MSD}-1VSD\\ & =\left(0.05\right)-\frac{19}{20}\cdot \left(0.05\right)=\frac{1}{20}\cdot \left(0.05\right)=0.0025cm\end{array}$