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. 0.1 mm
B. 0.5 mm
C. 0.4 mm
D. 1 mm

Explanation

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

### Step-by-Step Solution:

1. **Understanding the relationship between main scale divisions and vernier scale divisions:**
- We know that `50` vernier scale divisions (VSD) coincide with `49` main scale divisions (MSD). This can be expressed as:
\[ 50 \, \text{VSD} = 49 \, \text{MSD} \]

2. **Finding the value of one vernier scale division:**
- To find the value of one vernier scale division (VSD), we can express it in terms of main scale divisions:
\[ 1 \, \text{VSD} = \frac{49}{50} \, \text{MSD} \]

3. **Using the formula for the least count:**
- The least count (LC) of the vernier calipers is given by the formula:
\[ \text{LC} = 1 \, \text{MSD} - 1 \, \text{VSD} \]
- Substituting the expression for VSD from step 2 into the least count formula:
\[ \text{LC} = 1 \, \text{MSD} - \frac{49}{50} \, \text{MSD} \]

4. **Simplifying the least count expression:**
- Simplifying the expression gives:
\[ \text{LC} = 1 \, \text{MSD} - \frac{49}{50} \, \text{MSD} = \left(1 - \frac{49}{50}\right) \, \text{MSD} = \frac{1}{50} \, \text{MSD} \]

5. **Setting the least count equal to the given value:**
- We know the least count is `0.001 cm`, so we set up the equation:
\[ \frac{1}{50} \, \text{MSD} = 0.001 \, \text{cm} \]

6. **Solving for one main scale division:**
- To find the value of one main scale division (MSD), we multiply both sides of the equation by `50`:
\[ \text{MSD} = 0.001 \, \text{cm} \times 50 \]
- Calculating this gives:
\[ \text{MSD} = 0.05 \, \text{cm} \]

### Final Answer:
The value of one main scale division is `0.05 cm`.

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