A vernier caliper has a main scale with 2 divisions per millimeter. It is given that 50 vernier scale divisions coincide with 49 main scale divisions. When measuring the diameter of a spherical body, the zero of the vernier scale lies just after the 12.5 mm mark on the main scale, and the 24^ th vernier division coincides with a main scale division. If the instrument has a positive zero error of 0.04 mm , the true di

Step-by-step solution

The main scale has 2 divisions per millimeter. Length of one main scale division ( 1 MSD ) = 1 mm 2 = 0.5 mm Given that 50 VSD = 49 MSD 1 VSD = 49 50 MSD The least count (LC) of the vernier caliper is: LC = 1 MSD - 1 VSD LC = 1 MSD - 49 50 MSD = 1 50 MSD LC = 1 50 0.5 mm = 0.01 mm The measured reading is calculated as: Measured Reading = Main Scale Reading (MSR) + ( Vernier Scale Reading (VSR) LC ) Measured Reading = 12.5 mm + (24 0.01 mm ) = 12.5 mm + 0.24 mm = 12.74 mm The true reading is obtained by subtracting