One main scale division of a vernier calipers is ' a ' cm and \({n}^{\text{th }}\) division of the vernier scale coincid…

\[(n-1) M S D=n V S D \Rightarrow V S D=\frac{n-1}{n}(M S D)\]

Now, L.C \(=[1 \mathrm{MSD}-1 \mathrm{VSD}] \mathrm{cm}\)
\[\begin{aligned}& =a-\frac{n-1}{n} a=\frac{a}{n} \mathrm{~cm} \\& =\left(\frac{10 a}{n}\right) \mathrm{mm}\end{aligned}\]