Vernier constant is the (One or more than one correct option may be correct )

Options

A. (a)value of one MSD divided by total number of divisions on the main scale.
B. (b)value of one VSD divided by total number of divisions on the vernier scale.
C. (c)total number of divisions on the main scale divided by total number of divisions on the vernier scale.
D. (d)difference between the value of one main scale division and one vernier scale division.

Answer

### Step-by-Step Solution:

1. **Understanding Vernier Constant**: The Vernier constant is defined as the least count of the Vernier calipers. It is a crucial parameter that helps in measuring small lengths accurately.

2. **Definition of Least Count**: The least count of Vernier calipers is calculated using the formula:
\[ \text{Least Count} = \text{Value of one Main Scale Division (MSD)} - \text{Value of one Vernier Scale Division (VSD)} \]

3. **Analyzing the Options**:
- **Option A**: "Value of one main scale division divided by total number of divisions on the main scale."
- This does not represent the least count and is incorrect.
- **Option B**: "Value of one vernier scale division divided by total number of divisions on the vernier scale."
- This also does not represent the least count and is incorrect.
- **Option C**: "Total number of divisions on the main scale divided by total number of divisions on the vernier scale."
- This is a dimensionless quantity and does not give the least count, hence incorrect.
- **Option D**: "The difference between the value of one main scale division and one vernier scale division."
- This correctly defines the Vernier constant or least count of Vernier calipers.

4. **Conclusion**: The correct option that defines the Vernier constant is **Option D**.