$N$ divisions on the main scale of a vernier callipers coincide with $(N+1)$ divisions of the vernie

Question

$N$ divisions on the main scale of a vernier callipers coincide with $(N+1)$ divisions of the vernier scale. If each division of main scale is ' $a$ ' units, then the least count of the instrument is\

Professor PC Thomas Classes · Answer

(d) : $N \mathrm{MSD}=(N+1)$. VSD\ $1 \mathrm{VSD}=\frac{N}{N+1} \cdot \mathrm{MSD}$\ $\mathrm{LC}=1 \mathrm{MSD}-1 \mathrm{VSD}$\ $=1 \mathrm{MSD}-\frac{N}{N+1} \cdot \mathrm{MSD}=\frac{N+1-N}{N+1} \cdot \mathrm{MSD}$\ $=\frac{1}{N+1} \cdot a=\frac{a}{N+1} \quad(\because 1 \mathrm{MSD}=a$ units $)$\