# Least count of one big division on main scale is

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Updated on: September 25th, 2023

A transit’s main plate is divided into 1080 equal segments. The vernier’s 60 divisions exactly match the main plate’s 59 divisions. The transit can read angles accurate up to-

1. 5″
2. 10″
3. 15″
4. 20″
5. 30″

## 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

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