A vernier caliper has a least count of 0.05 mm and the value of one main scale division is 0.5 mm . If the vernier scale has 20 divisions in total, how many main scale divisions exactly coincide with the entire length of the vernier scale?

Step-by-step solution

Given, Least Count (LC) = 0.05 mm and 1 MSD = 0.5 mm . The least count is given by the difference between one main scale division and one vernier scale division: LC = 1 MSD - 1 VSD 0.05 mm = 0.5 mm - 1 VSD 1 VSD = 0.45 mm The total length of the vernier scale, which has 20 divisions, is: Total length = 20 1 VSD = 20 0.45 mm = 9.0 mm Let M be the number of main scale divisions that coincide with the entire vernier scale. Length of M main scale divisions = M 1 MSD = M 0.5 mm Equating the lengths: M 0.5 = 9.0 M = 9.0