Question

In a vernier callipers,'m' divisions of main scale coinvide with (m+1) divisions of vernier scale.If each division of main scale is 'd' units,the least count of instrument is

Answer 1

1/d is the least count

Answer 2

m MSD= (m+1) VSD
therefore,1VSD = (m/m-1 ) MSD
least count =1MSD -1VSD
= d - m/m-1 MSD
=d- m ×d/m-1
(taking m-1 as LCM)
=[d(m-1) - dm ]÷m-1
= [dm- d-dm]÷ m-1
= -d/m-1
hence, least count is -d/m-1
(MSD = main scale division)
(VSD =verniers scale division)