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. `0.02 mm`
B. b. `0.05 mm`
C. c. `0.1 mm`
D. d. `0.2 mm`

Explanation

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

### Step 1: Understand the formula for Least Count
The least count (LC) of a vernier caliper is given by the formula:
\[ \text{Least Count} = 1 \text{ Main Scale Division} - 1 \text{ Vernier Scale Division} \]

### Step 2: Identify the Main Scale Division (MSD)
From the problem, we know that:
- 1 Main Scale Division (MSD) = 1 mm

### Step 3: Determine the Vernier Scale Division (VSD)
We are given that:
- 20 divisions on the Vernier scale match with 16 divisions on the Main scale.

To find the value of one Vernier Scale Division (VSD), we can use the relationship:
\[ 20 \text{ VSD} = 16 \text{ MSD} \]

### Step 4: Calculate the value of one Vernier Scale Division
From the equation above, we can express one Vernier Scale Division as:
\[ 1 \text{ VSD} = \frac{16 \text{ MSD}}{20} \]

Substituting the value of MSD:
\[ 1 \text{ VSD} = \frac{16 \times 1 \text{ mm}}{20} = \frac{16}{20} \text{ mm} = \frac{4}{5} \text{ mm} = 0.8 \text{ mm} \]

### Step 5: Substitute values into the Least Count formula
Now we can substitute the values of MSD and VSD into the least count formula:
\[ \text{Least Count} = 1 \text{ MSD} - 1 \text{ VSD} \]
\[ \text{Least Count} = 1 \text{ mm} - 0.8 \text{ mm} \]
\[ \text{Least Count} = 0.2 \text{ mm} \]

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

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