One main scale division of a vernier callipers is 'a' cm and nᵗʰ division of the vernier scale coincide with (n - 1)ᵗʰ division of the main scale. The least count of the callipers in mm is :

Solution

Physics sir · 4 steps

Find the length of one vernier division first, then subtract it from one main scale division.

1. One vernier division. n vernier divisions cover the same length as (n-1) main scale divisions. So n × 1 VSD = (n-1)a, which gives 1 VSD = (n-1)a/n cm.
2. Least count. The least count is how much shorter one vernier division is than one main scale division.

   LC = 1 MSD - 1 VSD = a - (n-1)a/n = a/n cm

3. Convert to mm. Since 1 cm = 10 mm, multiply by 10: LC = 10a/n mm.
4. So. The least count is 10a/n mm, which is option (a).

The idea to keep. Least count is always 1 MSD minus 1 VSD. If n vernier divisions match (n-1) main divisions, the least count is 1 MSD divided by n. Convert units only at the end.

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