If `S and V` are one main scale and one Vernier scale and ` n - 1` divisions on the main scale are equivalent to `n` divisions of the Vernier , then

Options

A. The least count is `S//n`.
B. The Vernier constant is `S//n`.
C. The same Vernier constant can be used for circular Vernier also.
D. The same vernier constant cannot be used for circular Verniers.

Explanation

To solve the problem, we need to understand the relationship between the main scale (S) and the Vernier scale (V) in terms of their divisions. The question states that \( n - 1 \) divisions on the main scale are equivalent to \( n \) divisions on the Vernier scale.

### Step-by-Step Solution:

1. **Understanding the Given Information:**
- We have \( n - 1 \) divisions of the main scale (MSD) equal to \( n \) divisions of the Vernier scale (VSD).
- This can be expressed mathematically as:
\[ (n - 1) \times \text{MSD} = n \times \text{VSD} \]

2. **Finding the Value of One Vernier Scale Division (VSD):**
- Rearranging the above equation gives:
\[ \text{VSD} = \frac{(n - 1)}{n} \times \text{MSD} \]

3. **Calculating the Least Count (LC):**
- The least count of the Vernier scale is defined as:
\[ \text{Least Count} = \text{MSD} - \text{VSD} \]
- Substituting the value of VSD from the previous step:
\[ \text{Least Count} = \text{MSD} - \frac{(n - 1)}{n} \times \text{MSD} \]
- Simplifying this expression:
\[ \text{Least Count} = \text{MSD} \left(1 - \frac{(n - 1)}{n}\right) = \text{MSD} \left(\frac{1}{n}\right) \]

4. **Conclusion:**
- Therefore, we find that the least count of the Vernier scale is:
\[ \text{Least Count} = \frac{\text{MSD}}{n} \]
- Since the problem states that \( S \) is the main scale and \( V \) is the Vernier scale, we can conclude:
\[ \text{Least Count} = \frac{S}{n} \]

5. **Vernier Constant:**
- The Vernier constant is also equal to the least count, which we have derived as \( \frac{S}{n} \).

### Final Answer:
- The least count of the Vernier scale is \( \frac{S}{n} \).
- The Vernier constant is also \( \frac{S}{n} \).
- This can be used for circular Verniers as well.