Least count of one big division on main scale is

Answer: D. 20"

Least count of one big division on main scale is 20".

Solution:

Least count of one big division on the main scale(S) = Length of one big division/Total number of divisions

Least count of  a vernier scale is equal to the difference in length of one division of the main scale and one division of the vernier scale.

In a direct vernier (n-1) division of the main scale is equal to the n divisions on the vernier scale. Thus,

n.v=(n-1).S

v={(n-1)/n}S

Least count is given as,

L.C. = S-v

L.C. = S-{(n-1)/n}S

L.C. = S/n

Given: Total no. of divisions on main scale = 1080

Length of one division = 360º/1080

n= 60

L.C. = {(360º/1080)/60}×3600"=20"