A vernier callipers has 20 divisions on the vernier scale, which coincides with 19ᵗʰ division on the main scale. The least count of the instrument is 0.1 mm. One main scale division is equal to ________ mm.

Solution

Physics sir · 4 steps

Least count is one main scale division shared out over the 20 vernier divisions, so work backwards from it.

1. Size of one VSD. 20 vernier divisions cover 19 main scale divisions, so 20 VSD = 19 MSD. That gives 1 VSD = 19/20 MSD.
2. Least count. Least count is how much shorter one vernier division is than one main scale division.

   LC = 1 MSD - 1 VSD = (1 - 19/20)MSD = 1/20 MSD

3. Put in numbers. 1/20 MSD = 0.1 mm, so 1 MSD = 20 × 0.1 mm = 2 mm.
4. So. One main scale division is 2 mm, which is option (b).

The idea to keep. If n vernier divisions match (n-1) main scale divisions, then LC = MSD/n. Use it either way: find LC from MSD, or MSD from LC.

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