Question

In a Vernier caliper, N divisions of vernier scale coincide with (N-1) divisions of main scale (in which one division represents 1 mm). The least count of the instrument (in cm) should be :

• A. $N$
• B. $N-1$
• C. $\frac{1}{10N}$
• D. $\frac{1}{N-1}$

Answer 1

The correct option is C $\frac{1}{10N}$

Given, $NVernierScaleDivisions\left(VSD\right)=(N-1)MainScaleDivisions\left(MSD\right)$

$1VSD=\left(\frac{N-1}{N}\right)MSD$

$L.C=$ Least count $=1MSD-1VSD$

$L.C=(1-\frac{N-1}{N})MSD$

$=\frac{1}{N}MSD=\frac{0.1}{N}cm=\frac{1}{10N}cm$