A Vernier caliper is used to measure the diameter of a cylinder. It is given that 1 main scale division (MSD) is equal to 1 mm and 20 Vernier scale divisions (VSD) coincide with 19 main scale divisions. While taking the measurement, the zero of the Vernier scale lies just past the 3.1 cm mark on the main scale, and the 14^ th division of the Vernier scale coincides exactly with a main scale line. The diameter of the

Step-by-step solution

Least count (LC) of the Vernier caliper is given by: LC = 1 MSD - 1 VSD Given 20 VSD = 19 MSD , we have 1 VSD = 19 20 MSD . LC = 1 MSD - 19 20 MSD = 1 20 MSD Since 1 MSD = 1 mm , LC = 1 20 mm = 0.05 mm The main scale reading (MSR) is given as 3.1 cm , which is 31 mm . The Vernier scale reading (VSR) is the coinciding division multiplied by the least count: VSR = 14 0.05 mm = 0.70 mm Total reading = MSR + VSR = 31 mm + 0.70 mm = 31.70 mm Converting the final reading into cm: Diameter = 3.170 cm Answer: 3.170 cm