Question

A vernier callipers having $1$ main scale division = $0.1cm$ is designed to have a least count of $0.02cm$. If n be the number of divisions on vernier scale and $m$ be the length of vernier scale, then

• A. $n=10,m=0.5cm$
• B. $n=9,m=0.4cm$
• C. $n=10,m=0.8cm$
• D. $n=10,m=0.2cm$

Answer 1

Answer: (C)

$n=10,m=0.8cm$

$\begin{array}{c}\text{1.}MSD=0.01cm\\ \\ \text{L.C}=0.02cm\\ \text{least count}\end{array}$

$\begin{array}{c}\text{no of divisions on vernier scale}=n\\ \text{length of vernier scale}=m\\ \text{value of one vernier scale division}\\ 1VsD=\frac{m}{n}\\ \text{L.C}=1\text{MSD - IVSD}\end{array}$

$\begin{array}{c}0.02=0.1-\frac{m}{n}\\ \frac{m}{n\cdot }=0.1-0.02\\ \text{only one option satisfies above}\\ n=10m=0.8cm\end{array}$