1. Let one main scale division be $M$ mm.

2. Given: 20 vernier divisions coincide with 19 main scale divisions. Hence, $20\,\text{VSD} = 19\,\text{MSD}$ so $1\,\text{VSD} = \frac{19}{20}M$

3. For a direct vernier callipers, least count is $\text{L.C.} = 1\,\text{MSD} - 1\,\text{VSD}$

   Therefore, $\text{L.C.} = M - \frac{19}{20}M = \frac{1}{20}M$

4. Given least count = $0.1$ mm, so $\frac{1}{20}M = 0.1$ $M = 0.1 \times 20 = 2\,\text{mm}$

5. Thus one main scale division is $2\,\text{mm}$

6. Checking options:

   • A: $5$ mm ✗
   • B: $2$ mm ✓
   • C: $1$ mm ✗
   • D: $0.5$ mm ✗

Hence, the correct option is B.