Q 11-01-114JEE MainJEE Main 2024 (8 Apr, Shift 2)Medium
Least count of a vernier caliper is $\dfrac{1}{20N}\ \text{cm}$. The value of one division on the main scale is $1\ \text{mm}$. Then the number of divisions of main scale that coincide with $N$ divisions of vernier scale is:
Answer: (C) $\left(\dfrac{2N-1}{2}\right)$
Least count $= \dfrac{1}{20N}\ \text{cm} = \dfrac{1}{2N}\ \text{mm} = 1\ \text{MSD} - 1\ \text{VSD}$.
$$1\ \text{VSD} = 1 - \frac{1}{2N} = \frac{2N-1}{2N}\ \text{mm}$$
$$N\ \text{VSD} = \frac{2N-1}{2}\ \text{mm} = \frac{2N-1}{2}\ \text{MSD}$$
Solution by Sreeraj P, M.Sc Physics