N divisions on the main scale of a vernier callipers coincide with N+1 divisions on the vernier scale. If each division on the main scale is of a units determine the least count of the instrument.

(N+1) divisions on the vernier scale = N divisions on main scale1 division on vernier scale =NN+1 divisions on main scaleEach division on the main scale is of a units.1 division on vemier scale =NN+1a units=a' (say)Least count =1 main scale division -1 vernier scale divisionLeast count = a-a'=a-NN+1a=aN+1