Length of one division of main scale of a vernier calliper is 0.1 cm and that of scale is 0.9 cm. Find the value of vernier constant.

Options

A. 0.1 cm
B. 0.01 cm
C. 0.01 cm
D. 0.05 cm

Explanation

To find the value of the Vernier constant (also known as the least count) of a Vernier caliper, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Main Scale Division (MSD):**
The length of one division of the main scale (MSD) is given as:
\[ \text{MSD} = 0.1 \, \text{cm} \]

2. **Identify the Length of the Vernier Scale:**
The total length of the Vernier scale is given as:
\[ \text{Total length of Vernier scale} = 0.9 \, \text{cm} \]

3. **Determine the Number of Divisions on the Vernier Scale:**
Typically, a Vernier scale consists of 10 divisions unless specified otherwise. Therefore, we assume:
\[ \text{Number of divisions on Vernier scale} = 10 \]

4. **Calculate the Vernier Scale Division (VSD):**
The length of one division of the Vernier scale (VSD) can be calculated by dividing the total length of the Vernier scale by the number of divisions:
\[ \text{VSD} = \frac{\text{Total length of Vernier scale}}{\text{Number of divisions}} = \frac{0.9 \, \text{cm}}{10} = 0.09 \, \text{cm} \]

5. **Calculate the Vernier Constant:**
The Vernier constant is given by the formula:
\[ \text{Vernier Constant} = \text{MSD} - \text{VSD} \]
Substituting the values we have:
\[ \text{Vernier Constant} = 0.1 \, \text{cm} - 0.09 \, \text{cm} = 0.01 \, \text{cm} \]

### Final Answer:
The value of the Vernier constant is:
\[ \text{Vernier Constant} = 0.01 \, \text{cm} \]

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