In a certain vernier callipers, 10 divisions of the vernier scale coincide with 8 divisions of the main scale. The length of one main scale division is 1 mm. When measuring the diameter of a sphere, the zero of the vernier scale lies just after the 3.2 cm mark on the main scale, and the 4^ th division of the vernier scale exactly coincides with a main scale division. The measured diameter of the sphere is:

Step-by-step solution

First, we determine the least count (LC) of the vernier callipers. Given 10 VSD = 8 MSD, we have: 1 VSD = 8 10 MSD = 0.8 MSD Since 1 MSD = 1 mm, 1 VSD = 0.8 mm. The least count is: LC = 1 MSD - 1 VSD = 1 mm - 0.8 mm = 0.2 mm Converting the least count to cm: LC = 0.02 cm Now, we calculate the total reading for the diameter of the sphere. Main Scale Reading (MSR) = 3.2 cm Vernier Scale Reading (VSR) = 4 Total Reading = MSR + ( VSR LC ) Total Reading = 3.2 cm + (4 0.02 cm ) = 3.2 cm + 0.08 cm = 3.28 cm Answer: 3.28 c