The least count of a vernier caliper is y . The length of one main scale division is x . If N divisions of the vernier scale coincide with M divisions of the main scale, then the value of N is given by:

Step-by-step solution

The least count (L.C.) of a vernier caliper is given by the difference between one main scale division (MSD) and one vernier scale division (VSD). Given that 1 MSD = x and L.C. = y . Since N divisions of the vernier scale coincide with M divisions of the main scale, we have: N VSD = M MSD 1 VSD = M N MSD = M N x Now, substitute this into the least count formula: L.C. = 1 MSD - 1 VSD y = x - M N x Rearranging the terms to solve for N : M N x = x - y M N = x - y x N = Mx x - y Answer: Mx x-y