Question

The diameter of the spherical bob is measured using a vernier callipers. $9$ divisions of the main scale, in the vernier callipers, are equal to $10$ divisions of the vernier scale. One main scale division is $1\text{mm}$. The main scale reading is $10\text{mm}$ and $8^{th}$ division of vernier scale was found to coincide exactly with one of the main scale division. If the given vernier callipers has positive zero error of $0.04\text{cm}$, then the radius of the bob is ____
$\times {10}^{-2}\text{cm}$.

Answer 1

Given that $9$ divisions of the main scale, in the vernier callipers, are equal to $10$ divisions of vernier scale
i.e.
$9MSD=10VSD$
$9\text{mm}=10VSD$
$1VSD=0.9\text{mm}$

Least count of vernier is $LC=1MSD-1VSD=0.1\text{mm}$

Actual Reading $=MSR+(VSR\times LC)-\text{zero error}$

Reading of diameter is $d=10+(8\times 0.1)-0.4=10.4\text{mm}$

Radius of bob is $\frac{d}{2}=5.2\text{mm}=52\times {10}^{-2}\text{cm}$

Correct answer $:52$