Question

How would the precision of the measurement by vernier callipers be affected by

increasing the number of divisions on its vernier scale?​

Answer 1

Answer:

There is nothing to gain by increasing the vernier divisions. In fact, it will make the instrument less precise. The least count of the combination of a main & vernier scales is given by LC = 1 MSD - 1 VSD. If 1 main scale division is 1 mm and vernier scale has 10 divisions in 9 mm length, then 1 VSD will be 9/10 mm or 0.9 mm. Hence LC will be 1 mm - 0.9 mm = 0.1 mm.

Suppose that vernier has 20 divisions in 9 mm. Then each division will be 0.45 mm and LC will be 1 mm - 0.45 mm = 0.55 mm, which is greater than the earlier least count of 0.1 mm. Thus we have lost precision.