A vernier callipers has 20 divisions on the vernier scale which coincide with 19 divisions on the main scale. The least count of the instrument is 0.1 mm. The main scale divisions are of

Options

A. 0.5 mm
B. 1 mm
C. 2 mm
D. `1//4` mm

Explanation

To solve the problem, we need to find the main scale division (MSD) of the vernier calipers given the least count (LC) and the relationship between the divisions of the vernier scale (VS) and the main scale (MS).

### Step-by-Step Solution:

1. **Understand the relationship between the Vernier and Main Scale:**
- We know that 20 divisions on the Vernier scale coincide with 19 divisions on the main scale.
- This means that the length of 20 Vernier scale divisions is equal to the length of 19 main scale divisions.

2. **Calculate the length of one Vernier scale division (VSD):**
- The formula for one Vernier scale division is:
\[ \text{1 VSD} = \frac{19 \text{ MSD}}{20} \]

3. **Use the formula for Least Count (LC):**
- The least count of the instrument is given by the formula:
\[ \text{LC} = \text{1 MSD} - \text{1 VSD} \]
- We can substitute the expression for VSD into this formula:
\[ \text{LC} = \text{1 MSD} - \left(\frac{19 \text{ MSD}}{20}\right) \]

4. **Simplify the expression:**
- To simplify, we can express 1 MSD in terms of 20:
\[ \text{LC} = \frac{20 \text{ MSD}}{20} - \frac{19 \text{ MSD}}{20} = \frac{1 \text{ MSD}}{20} \]

5. **Set the Least Count equal to the given value:**
- We know from the problem that the least count is 0.1 mm:
\[ \frac{1 \text{ MSD}}{20} = 0.1 \text{ mm} \]

6. **Solve for the Main Scale Division (MSD):**
- Multiply both sides by 20 to find the MSD:
\[ 1 \text{ MSD} = 0.1 \text{ mm} \times 20 = 2 \text{ mm} \]

### Final Answer:
The main scale division (MSD) is **2 mm**.