A vernier callipers has a least count of 0.05 mm. The main scale is marked in half millimetres (i.e., 1 MSD = 0.5 mm). If the vernier scale has 50 divisions in total, how many main scale divisions coincide exactly with these 50 vernier scale divisions?

Step-by-step solution

The least count (LC) of a vernier callipers is given by the difference between the length of one main scale division (MSD) and one vernier scale division (VSD). LC = 1 MSD - 1 VSD Given that LC = 0.05 mm and 1 MSD = 0.5 mm, we can find the length of 1 VSD: 0.05 mm = 0.5 mm - 1 VSD 1 VSD = 0.5 mm - 0.05 mm = 0.45 mm The total length of the vernier scale, which has 50 divisions, is: Length of 50 VSD = 50 0.45 mm = 22.5 mm To find how many main scale divisions coincide with this length, we divide the total length of t