Name the two scales of a vernier callipers and explain, how it is used to measure a length correct up to 0.01 cm.

The two scales of a vernier callipers are —

1. Main scale - it is fixed
2. Vernier scale – slides along the main scale.

In the figure shown above, the main scale is graduated to read up to 1mm and the vernier scale has the length of 10 divisions equal to the length of 9 divisions of main scale.

Value of 1 division of main scale (x) = 1mm.

Total number of divisions on the vernier scale (n) = 10

Using the formula given below,

$\text{Least count (L.C.)} = \dfrac{\text{ Value of 1 main scale div (x)}}{\text {total no. of div on vernier (n)}}$

Substituting the value in the formula above, we get,

$\text{Least count (L.C.)} = \dfrac{\text{x}}{\text{n}} \\[0.5em] \text{Least count (L.C.)} = \dfrac{\text{1}}{\text{10}} \text{mm} \\[0.5em] \text{Least count (L.C.)} = 0.1\text{mm} \\[0.5em] \Rightarrow \text{Least count (L.C.)} = 0.01\text{cm} \\[0.5em]$

Hence, a vernier callipers is used to measure a length accurately up to 0.01cm.