Physics - Error Question with Solution | TestHub

Least count of vernier calipers $=\frac{1}{20\mathrm{N}}\mathrm{cm}$ $\because$ Least count $=1\mathrm{MSD}-1\mathrm{VSD}$ let $\mathrm{x}$ no. of divisions of main scale coincides with $\mathrm{N}$ division of vernier scale, then $\begin{array}{rl}& 1\mathrm{VSD}=\frac{\mathrm{x}\times 1\mathrm{mm}}{\mathrm{N}}\\ & \therefore \frac{1}{20\mathrm{N}}\mathrm{cm}=1\mathrm{mm}-\frac{\mathrm{x}\times 1\mathrm{mm}}{\mathrm{N}}\\ & \frac{1}{2\mathrm{N}}\mathrm{mm}=1\mathrm{mm}-\frac{\mathrm{x}}{\mathrm{N}}\mathrm{mm}\\ & \mathrm{x}=\left(1-\frac{1}{2\mathrm{N}}\right)\mathrm{N}\\ & \mathrm{x}=\frac{2\mathrm{N}-1}{2}\end{array}$