Physics - Practical physics Question with Solution | TestHub

As it is given that $\mathrm{n}$ divisions of vernier scale coincide with $(n-1)$ divisions of main scale i.e. $$\begin{array}{rl}& \mathrm{n}(\mathrm{VSD})=(\mathrm{n}-\mathrm{l})\text{ MSD }\\ & \Rightarrow \text{ IVSD }=\frac{(\mathrm{n}-\mathrm{l})}{\mathrm{n}}\mathrm{MSD}\\ & \end{array}$$ The least count is the difference between one main scale division (MSD) and one vernier scale division (VSD). $$\begin{array}{rl}& \therefore \text{ Least Count }(\mathrm{LC})=1\mathrm{MSD}-1\mathrm{lVSD}\\ & =1\mathrm{MSD}-\frac{(\mathrm{n}-\mathrm{l})}{\mathrm{n}}\mathrm{MSD}\\ & =\left(1-\frac{(\mathrm{n}-\mathrm{l})}{\mathrm{n}}\right)\mathrm{MSD}=\frac{1}{\mathrm{n}}\text{ MSD }\\ & \text{ Here, }1\mathrm{MSD}=\frac{1}{\mathrm{n}}\mathrm{cm}\\ & \Rightarrow \mathrm{LC}=\frac{\mathrm{l}}{\mathrm{n}}\times \frac{\mathrm{l}}{\mathrm{n}}\mathrm{cm}=\frac{\mathrm{l}}{{\mathrm{n}}^2}\mathrm{cm}\\ & \end{array}$$