Least count of a vernier caliper is 1/(20N) 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:
Options

Question

Least count of a vernier caliper is 1/(20N) 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:

G1 Physics · Accepted Answer

Least count: LC = 1 MSD - 1 VSD Given: LC = 1/(20N) cm Also: 1 MSD = 1 mm = 0.1 cm Let x main-scale divisions coincide with N vernier divisions. Then: 1 VSD = x(1 mm)/N Using millimetres: 1/(2N) mm = 1 mm - x/N mm Multiply by N: 1/2 = N - x Therefore: x = N - 1/2 = (2N - 1)/2