The Vernier constant of a Vernier Callipers is

Options

A. least count of Vernier callipers
B. Value of 1 division of main scale
C. value of 1 division of vernier scale
D. None of these

Answer

To solve the question regarding the Vernier constant of a Vernier caliper, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- The Vernier constant (Vc) is defined as the least count of the Vernier calipers. It is the smallest measurement that can be accurately read using the Vernier scale.

2. **Identify the Formula**:
- The Vernier constant can be calculated using the formula:
\[ Vc = 1 \text{ Main Scale Division (MSD)} - 1 \text{ Vernier Scale Division (VSD)} \]

3. **Express the Relationship**:
- If 'n' divisions on the Vernier scale coincide with 'n-1' divisions on the main scale, we can express this relationship mathematically:
\[ Vc = \text{MSD} - \left(\frac{n-1}{n} \times \text{MSD}\right) \]

4. **Simplify the Equation**:
- Rearranging the equation gives:
\[ Vc = \text{MSD} \left(1 - \frac{n-1}{n}\right) \]
- This simplifies to:
\[ Vc = \text{MSD} \left(\frac{1}{n}\right) \]

5. **Conclusion**:
- Therefore, the Vernier constant (Vc) is equal to the main scale division (MSD) divided by 'n', where 'n' is the number of divisions on the Vernier scale that coincide with 'n-1' divisions on the main scale.

### Final Answer:
The Vernier constant of a Vernier caliper is given by:
\[ Vc = \frac{\text{MSD}}{n} \]