1. Given data

• $10$ divisions on the main scale coincide with $11$ divisions on the Vernier scale.
• One main scale division (MSD) $= 5$ units.

So, $10\,\text{VSD} = 10\,\text{MSD}?$ But from the statement, $10\,\text{MSD} = 11\,\text{VSD}$

2. Find one Vernier scale division (VSD)

Since $10\,\text{MSD} = 11\,\text{VSD}$ we get $1\,\text{VSD} = \frac{10}{11}\,\text{MSD}$

Given $1\,\text{MSD} = 5\,\text{units}$ therefore $1\,\text{VSD} = \frac{10}{11}\times 5 = \frac{50}{11}\,\text{units}$

3. Least count of Vernier calliper

For a direct Vernier, $\text{Least Count} = 1\,\text{MSD} - 1\,\text{VSD}$

So, $\text{LC} = 5 - \frac{50}{11}$ $= \frac{55-50}{11} = \frac{5}{11}\,\text{units}$

4. Check options

• A: $\frac{5}{11}$ ✅
• B: $\frac{10}{11}$ ❌
• C: $\frac{50}{11}$ ❌
• D: $\frac{1}{2}$ ❌

Hence, the correct answer is: $\boxed{\frac{5}{11}}$