Chapter 2: Units and Measurements
Precision measurement is fundamental to experimental physics. The ordinary metric scale has a least count of $1 ext{ mm}$. To measure lengths with precision up to $0.1 ext{ mm}$ or $0.01 ext{ cm}$, a Vernier Caliper is used.
1. Least Count (Vernier Constant)
Least Count (LC) is the smallest value that can be measured directly with the instrument.
$$ ext{L.C.} = 1 ext{ M.S.D.} - 1 ext{ V.S.D.} = rac{ ext{Value of 1 Main Scale Division}}{ ext{Total number of Vernier Scale Divisions}}$$
For standard calipers where $10$ Vernier divisions coincide with $9$ main scale divisions ($9 ext{ mm}$):
$$ ext{L.C.} = 1 ext{ mm} - 0.9 ext{ mm} = 0.1 ext{ mm} = 0.01 ext{ cm}$$
2. Total Reading Calculation
$$ ext{Total Reading} = ext{M.S.R.} + ( ext{V.S.D. Coincidence} imes ext{L.C.}) \pm ext{Zero Correction}$$