1. Given data

• Main scale least count: $1\text{ mm} = 0.1\text{ cm}$
• $10$ vernier scale divisions coincide with $9$ main scale divisions.

So, $10\,\text{VSD} = 9\,\text{MSD}$

Since $1\,\text{MSD} = 1\text{ mm},$ we get $1\,\text{VSD} = \frac{9}{10}\text{ mm} = 0.9\text{ mm}.$

Hence the vernier least count is $\text{LC} = 1\,\text{MSD} - 1\,\text{VSD} = 1 - 0.9 = 0.1\text{ mm} = 0.01\text{ cm}.$

2. Find the zero error

When jaws are closed:

• zero of vernier is to the right of zero of main scale,
• 7th vernier division coincides with a main scale division.

This means the instrument has a positive zero error.

For a direct vernier, if the $n$th vernier division coincides, then zero reading is $n \times \text{LC}.$

So zero error is $7 \times 0.1\text{ mm} = 0.7\text{ mm} = 0.07\text{ cm}.$

Thus, $\text{Zero error} = +0.07\text{ cm}.$

Therefore zero correction is $-0.07\text{ cm}.$

3. Observed reading of the cylinder

The zero of vernier lies between $3.1\text{ cm}$ and $3.2\text{ cm}$, so the main scale reading is $\text{MSR} = 3.1\text{ cm}.$

Also, the 4th vernier scale division coincides. So vernier reading is $\text{VR} = 4 \times \text{LC} = 4 \times 0.01 = 0.04\text{ cm}.$

Hence observed reading is $\text{Observed reading} = 3.1 + 0.04 = 3.14\text{ cm}.$

4. Apply zero correction

Since zero error is positive, true reading is $\text{True reading} = \text{Observed reading} - \text{Zero error}$ $= 3.14 - 0.07 = 3.07\text{ cm}.$

5. Check options

• A: $3.21\text{ cm}$ ❌
• B: $2.99\text{ cm}$ ❌
• C: $3.07\text{ cm}$ ✅
• D: $3.2\text{ cm}$ ❌

So the correct option is C.