The vernier constant of a vernier callipers is `0.001 cm`. If `49` main scale divisions coincide with `50` vernier scale devisions, then the value of `1` main scale divisions is .

Options

A. `0.1m`
B. `0.5m`
C. `0.4m`
D. `1mm`

Answer

To solve the problem, we need to find the value of one main scale division (MSD) given that 49 main scale divisions coincide with 50 vernier scale divisions (VSD) and the vernier constant (least count) is 0.001 cm.

### Step-by-Step Solution:

1. **Understanding the relationship between MSD and VSD**:
We know that:
\[ 50 \text{ VSD} = 49 \text{ MSD} \]
This means that the length of 50 vernier scale divisions is equal to the length of 49 main scale divisions.

2. **Let the value of one main scale division be \( x \) cm**:
We will denote the value of one main scale division as \( x \) cm.

3. **Finding the value of one vernier scale division**:
Since 50 VSD equals 49 MSD, we can express the value of one vernier scale division (VSD) in terms of \( x \):
\[ 1 \text{ VSD} = \frac{49}{50} \times x \text{ cm} \]

4. **Using the least count formula**:
The least count (LC) is defined as:
\[ \text{LC} = 1 \text{ MSD} - 1 \text{ VSD} \]
Substituting the values we have:
\[ 0.001 \text{ cm} = x - \left(\frac{49}{50} \times x\right) \]

5. **Simplifying the equation**:
We can simplify the right side:
\[ 0.001 = x - \frac{49x}{50} \]
This can be rewritten as:
\[ 0.001 = \frac{50x - 49x}{50} = \frac{x}{50} \]

6. **Solving for \( x \)**:
To find \( x \), we multiply both sides by 50:
\[ x = 0.001 \times 50 \]
\[ x = 0.05 \text{ cm} \]

7. **Conclusion**:
Therefore, the value of one main scale division is:
\[ \boxed{0.05 \text{ cm}} \]