Question

Assertion: The least count of Vernier calipers is dependent on its design.
Reason:
 $ The{\text{ }}L.C.{\text{ }}of{\text{ }}V.C.{\text{ }} = \dfrac{{Pitch}}{{No.{\text{ }}of{\text{ }}V.S.D.}} $
(A) Both assertion and reason are correct and reason is the correct explanation for Assertion.
(B)Both assertion and reason are correct but reason is not the correct explanation for Assertion.
(C) Assertion is correct but reason is incorrect.
(D)Assertion is incorrect but reason is correct.

Answer 1

Hint :In order to solve this question, we are going to first define what the least count for any instrument is. Then, the mathematical form of the least count expression which defines it even more. And hence, the assertion and reason are judged on the basis of this theory and the question is answered.

Complete Step By Step Answer:
The least count of a measuring instrument is the smallest and accurate value in the measured quantity that can be resolved on the instrument’s scale .The least count is related to the precision of an instrument, an instrument that can measure smaller changes in a value relative to another instrument has a smaller least count value and so is more precise.
The mathematical relation for the least count is given by:
 $ L.C = 1M.S.D. - 1V.S.D. $
Where,
 $ M.S.D. = Main{\text{ }}scale{\text{ }}division \\
  V.S.D = Vernier{\text{ }}scale{\text{ }}division \\ $
Another form of this expression can be written as
 $ The{\text{ }}L.C.{\text{ }}of{\text{ }}V.C.{\text{ }} = \dfrac{{Pitch}}{{No.{\text{ }}of{\text{ }}V.S.D.}} $
Thus, the least count depends upon how many divisions of the Vernier scale coincide with how many divisions of the main scale. Thus, the design of Vernier calipers is important to count.
Hence, option (A) is the correct answer.

Note :
The least count of Vernier calipers depend on its extraordinary design, which helps it to make such small and precise measurements. Also it depends upon the pitch and the number of the Vernier scale divisions present on the caliper.