The main scale of a circular vernier instrument has N divisions per degree. It is given that V divisions of the vernier scale coincide with (V-1) divisions of the main scale. The least count of the instrument in minutes is

Step-by-step solution

The main scale has N divisions per degree. Therefore, the value of one main scale division (MSD) is: 1 MSD = 1 N degrees Since 1 degree = 60 minutes , we can express 1 MSD in minutes: 1 MSD = 60 N minutes It is given that V divisions of the vernier scale coincide with (V-1) divisions of the main scale: V VSD = (V-1) MSD 1 VSD = V-1 V MSD The least count (LC) is the difference between one MSD and one VSD: LC = 1 MSD - 1 VSD LC = 1 MSD - V-1 V MSD = 1 V MSD Substituting the value of 1 MSD in minutes: LC = 1 V ( 60 N