Least count of a vernier caliper is 1/(20 N) cm. The value of one division on the main scale is 1 mm. Then the number of divisions of main scale that coincide with N divisions of vernier scale is :

Solution

Physics sir · 4 steps

Convert the least count to millimetres first, then use LC = 1 MSD − 1 VSD to find one vernier division.

1. Least count in mm. The main scale is read in mm, so convert: 1/20N cm = 10/20N mm = 1/2N mm.

   LC = 1 MSD - 1 VSD

2. One vernier division. With 1 MSD = 1 mm, we get 1 VSD = 1 - 1/2N = (2N-1)/2N mm.
3. N vernier divisions. Multiply by N: N VSD = N × (2N-1)/2N = (2N-1)/2 mm. Each main scale division is 1 mm, so this length covers (2N-1)/2 main scale divisions.
4. So. N vernier divisions coincide with ((2N-1)/2) main scale divisions, which is option (d).

The idea to keep. For any vernier, least count is one main scale division minus one vernier division. Put everything in the main scale's unit before you subtract.

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