One main scale division of a vernier caliper is equal to m units. If nᵗʰ division of main scale coincides with (n+1)ᵗʰ division of vernier scale, the least count of the vernier caliper is :

Solution

Physics sir · 3 steps

Find one vernier division in main-scale units first, then subtract it from one main-scale division.

1. Equal lengths. n main scale divisions cover the same length as (n+1) vernier divisions. One main scale division is m, so that length is nm.
2. One vernier division. Share that length over (n+1) divisions: 1 VSD = nm/(n+1). This is a little shorter than m.

   LC = 1 MSD - 1 VSD = m - nm/(n+1) = (m(n+1) - nm)/(n+1) = m/(n+1)

3. So. The least count is m/(n+1), which is option (b).

The idea to keep. Least count is always 1 MSD minus 1 VSD. Turn the coinciding divisions into one length equation, find 1 VSD from it, and keep the size of the MSD in your answer.

Answer from the NTA final answer key. Solution by PrepWiser.