The vernier scale of a travelling microscope has 50 divisions which coincide with 49 main scale divisions. If each main scale division is 0.5 mm, calculate the minimum inaccuracy in the measurement of distance.

The correct option is 0.01 mm.

Step-by-step Explanation:

1. Understand the concept of minimum inaccuracy:
The minimum inaccuracy in the measurement of a distance using a vernier instrument is equal to its least count (LC). The least count is the smallest value that can be measured accurately by the instrument and is given by the difference between one main scale division (MSD) and one vernier scale division (VSD).

2. Identify the given parameters:
- Value of 1 main scale division (MSD) = 0.5 mm
- Number of vernier scale divisions (N) = 50 divisions
- These 50 vernier scale divisions coincide with 49 main scale divisions.

3. Calculate the value of 1 vernier scale division (VSD):
Since 50 VSD = 49 MSD, we can find the value of 1 VSD as follows:
$$1\text{ VSD}=\frac{49}{50}\text{ MSD}$$
Substituting the value of 1 MSD = 0.5 mm:
$$1\text{ VSD}=\frac{49}{50}\times 0.5\text{ mm}=0.49\text{ mm}$$

4. Calculate the least count (LC) or minimum inaccuracy:
The least count is calculated using the formula:
$$\text{Least Count (LC)}=1\text{ MSD}-1\text{ VSD}$$
Substitute the values into the formula:
$$\text{LC}=0.5\text{ mm}-0.49\text{ mm}=0.01\text{ mm}$$

Alternatively, the least count can also be calculated using the direct formula:
$$\text{LC}=\frac{\text{Value of 1 MSD}}{\text{Total number of divisions on the vernier scale}}$$
Using this formula:
$$\text{LC}=\frac{0.5\text{ mm}}{50}=0.01\text{ mm}$$
Therefore, the minimum inaccuracy in the measurement of distance is 0.01 mm.