Question

Let main scale division of a Vernier callipers is $1mm.$ With zero of Vernier coinciding with the zero of main scale, the ${50^{th}}$ division of Vernier scale coincides with ${49^{th}}$ division of main scale. The least count of the Vernier is
(A) $0.1mm$
(B) $0.01mm$
(C) $0.2mm$
(D) $0.02mm$

Answer 1

Hint
To find the least count of the Vernier scale we must know the least count calculation for an equipment. Least count is the smallest measurement that could be measured with an equipment.

Complete step by step answer
Vernier calliper was discovered by Pierre Vernier of France. The modern Vernier calliper was invented by Joseph R. Brown. It was the first practical tool for exact measurements that is sold at an affordable price.
A calliper is a device used to measure the width of an object. It is as simple as a compass.
The Vernier scale has two graduated scales namely main scale and Vernier scale. Main scale is the one which is similar to the meter scale we use for measurement and the Vernier scale is the one which lies on the mains scale. The main scale is fixed and the Vernier scale is movable. Vernier callipers are used in laboratories and in manufacturing for quality control measurements.
The least count is the smallest reading which you can measure with the instrument.
The least count of the Vernier scale is given by the difference between the value of one main scale division and the value of one Vernier scale division.
Given that,
The main scale division of a Vernier callipers is $1mm.$
The ${50^{th}}$ division of Vernier scale coincides with ${49^{th}}$ division of main scale, so the value of one Vernier scale division is $\dfrac{{49}}{{50}} \times 1{\text{ = }}\dfrac{{49}}{{50}}mm$
The least count $ = {\text{ 1 }} - {\text{ }}\dfrac{{{\text{49}}}}{{50}}$
$ \Rightarrow \dfrac{1}{{50}}mm$
 $ \Rightarrow 0.02mm$
Hence the correct answer is option (D); $0.02mm$.

Note
Least count is constant for a device. It does not change from time to time the least count is not affected by any other external factors.