Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: If in five complete rotations of the circular scale, the distance travelled on the main scale of the screw gauge is $5$ mm and there are $50$ total divisions on a circular scale, then the least count is $0.001$ cm.
Reason $R$: Least count $= \dfrac{\text{Pitch}}{\text{Total divisions on circular scale}}$
In the light of the above statements, choose the most appropriate answer from the options given below.
Answer: (A) $A$ is not correct but $R$ is correct.
Pitch $= \dfrac{5\ \text{mm}}{5} = 1$ mm.
Least count $= \dfrac{1\ \text{mm}}{50} = 0.02$ mm $= 0.002$ cm, not $0.001$ cm. So $A$ is wrong.
The formula in $R$ is the correct definition of least count, so $R$ is correct.
Solution by Sreeraj P, M.Sc Physics