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. ` (a)9 mm` divided into 10 divisions.
B. `(b)90 mm` divided into 100 divisions.
C. `(c)99 mm` divided into 100 divisions
D. `(d)9 mm` divided into 100 divisions.

Explanation

To solve the problem of determining which vernier scale gives a vernier constant equal to 0.01 mm, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- Each division on the main scale (MSD) is 1 mm.
- We need to find a vernier scale (VSD) that gives a vernier constant (VC) of 0.01 mm.

2. **Use the Formula for Vernier Constant**:
- The formula for the vernier constant (least count) is given by:
\[ \text{Vernier Constant (VC)} = \text{One Main Scale Division (MSD)} - \text{One Vernier Scale Division (VSD)} \]
- Rearranging this gives us:
\[ \text{One Vernier Scale Division (VSD)} = \text{One Main Scale Division (MSD)} - \text{Vernier Constant (VC)} \]

3. **Substitute the Known Values**:
- We know that:
- One MSD = 1 mm
- VC = 0.01 mm
- Substituting these values into the equation:
\[ \text{One VSD} = 1 \text{ mm} - 0.01 \text{ mm} = 0.99 \text{ mm} \]

4. **Check the Options**:
- Now we need to check which of the given options provides a VSD of 0.99 mm.
- **Option A**: 9 mm divided into 10 divisions:
\[ \text{VSD} = \frac{9 \text{ mm}}{10} = 0.9 \text{ mm} \quad (\text{Not Correct}) \]
- **Option B**: 90 mm divided into 100 divisions:
\[ \text{VSD} = \frac{90 \text{ mm}}{100} = 0.9 \text{ mm} \quad (\text{Not Correct}) \]
- **Option C**: 99 mm divided into 100 divisions:
\[ \text{VSD} = \frac{99 \text{ mm}}{100} = 0.99 \text{ mm} \quad (\text{Correct}) \]
- **Option D**: 9 mm divided into 100 divisions:
\[ \text{VSD} = \frac{9 \text{ mm}}{100} = 0.09 \text{ mm} \quad (\text{Not Correct}) \]

5. **Conclusion**:
- The only option that gives a vernier scale division of 0.99 mm is **Option C**.

### Final Answer:
The correct answer is **Option C** (99 mm divided into 100 divisions).

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