Each division on the main scale is `1 mm`. Which of the following vernier scales give vernier constant equal to `0.01 mm`?

Options

A. `9mm` divided into 10 divisions
B. `90mm` divided into 10 divisions
C. `99 mm` divided into 100 divisions
D. none of these

Answer

To solve the problem, we need to determine which Vernier scale gives a Vernier constant equal to 0.01 mm when each division on the main scale is 1 mm.

### Step-by-Step Solution:

1. **Understand the Definitions**:
- The **Vernier Constant (VC)** is defined as:
\[ VC = \frac{1 \text{ Main Scale Division (MSD)}}{\text{Number of divisions on the Vernier Scale (n)}} \]
- In this case, the Main Scale Division (MSD) is given as 1 mm.

2. **Set Up the Equation**:
- We know that the Vernier Constant is equal to 0.01 mm. Therefore, we can set up the equation:
\[ VC = \frac{1 \text{ mm}}{n} = 0.01 \text{ mm} \]

3. **Solve for n**:
- Rearranging the equation to solve for \( n \):
\[ n = \frac{1 \text{ mm}}{0.01 \text{ mm}} = 100 \]
- This means that the Vernier scale must have 100 divisions.

4. **Conclusion**:
- Since we found that the number of divisions on the Vernier scale (n) must be 100 in order to achieve a Vernier constant of 0.01 mm, we can conclude that the correct option is the one that indicates a Vernier scale with 100 divisions.

### Final Answer:
- The correct option is **C**, which corresponds to a Vernier scale with 100 divisions.