Q 11-01-117JEE MainJEE Main 2024 (9 Apr, Shift 1)Easy
One main scale division of a vernier caliper is equal to $m$ units. If the $n^{\text{th}}$ division of main scale coincides with the $(n+1)^{\text{th}}$ division of vernier scale, the least count of the vernier caliper is:
Answer: (C) $\dfrac{m}{n+1}$
$(n+1)$ vernier divisions equal $n$ main scale divisions:
$$1\ \text{VSD} = \frac{n}{n+1}\ \text{MSD} = \frac{nm}{n+1}$$
$$\text{LC} = 1\ \text{MSD} - 1\ \text{VSD} = m - \frac{nm}{n+1} = \frac{m}{n+1}$$
Solution by Sreeraj P, M.Sc Physics