Question

The main scale of a vernier calliper is a half-millimetre scale. $50$ vernier divisions coincide with $49$ main scale divisions. What is the vernier constant of the system?

Answer 1

Step 1: Given data

$50VSD\equiv 49MSD$

Here , $VSD=Vernierscaledivision,MSD=Mainscaledivision$
Therefore, $1VSD=\frac{49}{50}MSD$

Step 2: calculating least count of the instrument
Least count of the instrument =$MSD-VSD=MSD\times (1-\frac{49}{50})$
( If MSD is given as $0.5mm$)
Hence, least count of vernier callipers =$0.5\times \left(\frac{1}{50}\right)=\frac{1}{25}mm=0.01mm$

Hence, vernier constant of the system is $0.01mm.$