A vernier callipers has 20 divisions on the vernier scale, which coincides with 19th division on the main scale. The least count of the instrument is 0.1 mm. One main scale division is equal to ____mm.
- 1
- 0.5
- 2
- 5
The Correct Option is C
Solution and Explanation
Given:
- 20 vernier scale divisions (VSD) coincide with 19 main scale divisions (MSD).
- Least count (L.C.) of the instrument is \( 0.1 \, \text{mm} \).
Step 1: Relation Between VSD and MSD
From the given data:
\[ 20 \, \text{VSD} = 19 \, \text{MSD}. \]
The value of one vernier scale division (1 VSD) is:
\[ 1 \, \text{VSD} = \frac{19}{20} \, \text{MSD}. \]
Step 2: Calculating the Least Count
The least count (L.C.) is given by:
\[ \text{L.C.} = 1 \, \text{MSD} - 1 \, \text{VSD}. \]
Substituting the value of 1 VSD:
\[ \text{L.C.} = 1 \, \text{MSD} - \frac{19}{20} \, \text{MSD} = \frac{1}{20} \, \text{MSD}. \]
Given that the least count is \( 0.1 \, \text{mm} \):
\[ 0.1 \, \text{mm} = \frac{1}{20} \, \text{MSD}. \]
Multiplying both sides by 20:
\[ 1 \, \text{MSD} = 2 \, \text{mm}. \]
Therefore, one main scale division is equal to \( 2 \, \text{mm} \).
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