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 radius of the cylinder is $1.76\times {10}^{-x}m$. 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 $1-\frac{19}{20}mm=0.05mm=0.005cm$

Main scale reading $=35mm$

$=3.5cm$

Vernier scale reading $=4$

Vernier scale reading X L.C $=4$ X $0.05=0.2mm$

$=0.02cm$

Total reading $=3.5+0.02$

$=3.52cm$

Radius of cylinder $=\frac{3.52}{2}=1.76cm$

$\Rightarrow x=2$