# The least count of the main scale of a vernier callipers

Question:

The least count of the main scale of a vernier callipers is $1 \mathrm{~mm}$. 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 vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of a cylinder the zero of the vernier scale between $3.1 \mathrm{~cm}$ and $3.2 \mathrm{~cm}$ and $4^{\text {th }}$ VSD coincides with a main scale division. The length of the cylinder is : (VSD is vernier scale division)

1. $3.21 \mathrm{~cm}$

2. $2.99 \mathrm{~cm}$

3. $3.2 \mathrm{~cm}$

4. $3.07 \mathrm{~cm}$

Correct Option: , 4

Solution:

Least count $=1 \mathrm{~mm}$ or $0.01 \mathrm{~cm}$

Zero error $=0+0.01 \times 7=0.07 \mathrm{~cm}$

Reading $=3.1+(0.01 \times 4)-0.07$

$=3.1+0.04-0.07$

$=3.1-0.03$

$=3.07 \mathrm{~cm}$