Given data

• $50$ Vernier scale divisions $= 49$ main scale divisions
• One main scale division (MSD) $= 0.5\,\text{mm}$

Find the value of one Vernier scale division (VSD)

Since $50$ VSD $= 49$ MSD, $1\,\text{VSD} = \frac{49}{50}\,\text{MSD}$

Substituting $1\,\text{MSD} = 0.5\,\text{mm}$, $1\,\text{VSD} = \frac{49}{50} \times 0.5 = 0.49\,\text{mm}$

Vernier constant / least count

For a direct vernier, $\text{Vernier constant} = 1\,\text{MSD} - 1\,\text{VSD}$

Therefore, $\text{VC} = 0.5 - 0.49 = 0.01\,\text{mm}$

Match with options

• A: $0.01\,\text{mm}$ ✅
• B: $0.01\,\text{cm} = 0.1\,\text{mm}$ ❌
• C: $0.1\,\text{mm}$ ❌
• D: $0.1\,\text{cm} = 1\,\text{mm}$ ❌

Final answer $\boxed{0.01\,\text{mm}}$ So, the correct option is A.