In a vernier caliper, 1 cm on the main scale is divided into 10 equal parts. It is given that 20 divisions of the vernier scale coincide with 19 divisions of the main scale. While measuring the diameter of a wire, the zero of the vernier scale lies between 2.3 cm and 2.4 cm on the main scale, and the 6^ th division of the vernier scale perfectly coincides with a main scale division. The diameter of the wire is:

Step-by-step solution

Value of one main scale division, 1 MSD = 1 cm 10 = 0.1 cm . Given that 20 VSD = 19 MSD , we have 1 VSD = 19 20 MSD . The least count (LC) of the vernier caliper is: LC = 1 MSD - 1 VSD = 1 MSD - 19 20 MSD = 1 20 MSD LC = 0.1 cm 20 = 0.005 cm The main scale reading (MSR) is 2.3 cm (since the vernier zero lies between 2.3 and 2.4 cm ). The vernier scale reading (VSR) is given by the coinciding division multiplied by the least count: VSR = 6 0.005 cm = 0.030 cm Total reading = MSR + VSR = 2.3 cm + 0.030 cm = 2.330 cm