A vernier calipers has `1mm `marks on the main scale. It has `20` equal divisions on the Verier scale which match with `16` main scale divisions. For this Vernier calipers, the least count is

Options

A. (a) `0.02mm`
B. (b) `0.05mm`
C. ( c ) `0.1mm`
D. (d) `0.2mm`

Explanation

To find the least count of the given vernier calipers, we can follow these steps:

### Step 1: Understand the given data
- The main scale has divisions of `1 mm`.
- The vernier scale has `20 divisions` that coincide with `16 divisions` of the main scale.

### Step 2: Calculate the value of one division of the vernier scale
Since `20 divisions of the vernier scale` are equal to `16 divisions of the main scale`, we can express this mathematically:
\[ 20 \, \text{Vernier Scale Divisions} = 16 \, \text{Main Scale Divisions} \]
To find the value of one division of the vernier scale (VSD), we can write:
\[ 1 \, \text{VSD} = \frac{16 \, \text{MSD}}{20} \]
Where MSD is the main scale division.

### Step 3: Substitute the value of the main scale division
Since the main scale division is `1 mm`, we can substitute:
\[ 1 \, \text{VSD} = \frac{16 \times 1 \, \text{mm}}{20} = \frac{16}{20} \, \text{mm} = 0.8 \, \text{mm} \]

### Step 4: Calculate the least count
The least count (LC) of the vernier calipers is given by the formula:
\[ \text{Least Count} = \text{1 MSD} - \text{1 VSD} \]
Substituting the values we have:
\[ \text{Least Count} = 1 \, \text{mm} - 0.8 \, \text{mm} = 0.2 \, \text{mm} \]

### Final Answer
Thus, the least count of the vernier calipers is:
\[ \text{Least Count} = 0.2 \, \text{mm} \]

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