The least count of the main scale of a vernier callipers is $1\ \text{mm}$. Its vernier scale is divided into $10$ divisions and coincide with $9$ divisions of the main scale. When jaws are touching each other, the $7^{\text{th}}$ division of the vernier scale coincides with a division of the main scale and the zero of vernier scale is lying right side of the zero of the main scale. When this vernier is used to measure the length of the cylinder the zero of the vernier scale is between $3.1\ \text{cm}$ and $3.2\ \text{cm}$ and $4^{\text{th}}$ VSD coincides with the main scale division. The length of the cylinder is (VSD is vernier scale division)
Answer: (C) $3.07\ \text{cm}$
Least count $= 1\ \text{MSD} - 1\ \text{VSD} = 1 - 0.9 = 0.1$ mm $= 0.01$ cm.
Zero error: vernier zero is to the right, so the error is positive: $+7\times0.01 = +0.07$ cm.
Observed reading $= 3.1 + 4\times0.01 = 3.14$ cm. Corrected length $= 3.14 - 0.07 = 3.07$ cm.
Solution by Sreeraj P, M.Sc Physics