Question

The main scale of a vernier callipers is calibrated in mm and 19 divisions of main scale are equal in length to 20 divisions of vernier scale. In measuring the diameter of a cylinder by this instrument, the main scale reads 35 divisions and 4th division of vernier scale coincides with a main scale division. The least count is $5\times {10}^{-x}cm$. Find the value of $x$.

Answer 1

$20$ vernier scale division coincide with $19mm$ main scale divisions.

$1$ vernier scale division will coincide with $\frac{19}{20}mm$ main scale divisions.

Thus, $LC$ of vernier scale is $1-\frac{19}{20}mm=0.05mm=0.005cm$

$\Rightarrow x=3$