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

Options

A. (a) 0.1 mm
B. (b) 0.5 mm
C. (c)0.4 mm
D. (d)1 mm

Explanation

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

### Step-by-Step Solution:

1. **Understand 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. **Calculate the value of one vernier scale division**:
- From the above relationship, we can find the value of one vernier scale division (VSD) in terms of main scale divisions (MSD):
\[ 1 \, \text{VSD} = \frac{49}{50} \, \text{MSD} \]

3. **Use the formula for least count**:
- The least count (LC) of the vernier calipers is given by the formula:
\[ \text{Least Count} = 1 \, \text{MSD} - 1 \, \text{VSD} \]

4. **Substitute the value of one vernier scale division**:
- We can substitute the value of 1 VSD from step 2 into the least count formula:
\[ \text{Least Count} = 1 \, \text{MSD} - \left(\frac{49}{50} \, \text{MSD}\right) \]
- This simplifies to:
\[ \text{Least Count} = 1 \, \text{MSD} - \frac{49}{50} \, \text{MSD} = \frac{1}{50} \, \text{MSD} \]

5. **Set the least count equal to the given vernier constant**:
- We know from the problem that the least count is also equal to the vernier constant:
\[ \frac{1}{50} \, \text{MSD} = 0.001 \, \text{cm} \]

6. **Solve for one main scale division**:
- To find the value of one main scale division, we can rearrange the equation:
\[ \text{MSD} = 50 \times 0.001 \, \text{cm} = 0.05 \, \text{cm} \]

7. **Convert the result to millimeters**:
- Since 1 cm = 10 mm, we convert 0.05 cm to millimeters:
\[ 0.05 \, \text{cm} = 0.05 \times 10 \, \text{mm} = 0.5 \, \text{mm} \]

### Final Answer:
The value of one main scale division is **0.5 mm**.

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