The diameter of a spherical bob is measured using a vernier callipers. $9$ divisions of the main scale, in the vernier callipers, are equal to $10$ divisions of vernier scale. One main scale division is $1$ mm. The main scale reading is $10$ mm and $8^{\text{th}}$ division of vernier scale was found to coincide exactly with one of the main scale divisions. If the given vernier callipers has positive zero error of $0.04$ cm, then the radius of the bob is ______ $\times10^{-2}$ cm.
Numerical value type. Enter your answer.
Answer: 52
Least count $= 1\ \text{MSD} - 1\ \text{VSD} = 1 - 0.9 = 0.1$ mm.
Observed reading $= 10 + 8\times0.1 = 10.8$ mm $= 1.08$ cm.
Corrected diameter $= 1.08 - 0.04 = 1.04$ cm, so radius $= 0.52$ cm $= 52\times10^{-2}$ cm.
Solution by Sreeraj P, M.Sc Physics