Question

Vernier caliper has its main scale 10 cm equally divided into 250 parts. Its vernier scale is of 50 divisions and coincides with 15 mm of the main scale. The least count of the instrument is:
A. 0.01 cm
B. 0.02 cm
C. 0.001 cm
D. 0.002 cm

Answer 1

Hint: A caliper is an instrument used to measure the distance between two opposite sides of an object. While the vernier scale is a visual aid used to measure reading between two graduations marking on a linear scale using mechanical interpolation to reduce human error.
The vernier scale is used in a vernier caliper is to measure the internal and external diameter of an object. This vernier scale is constructed so that it is spaced at a constant fraction of the fixed main scale.
In this question, first, find out the Main scale divisions and the vernier scale division the Find the Least count.

Complete step by step answer:
The main scale is 10 cm equally divided into 250 parts, where 1 Main scale division is defined as the distance between the two successive marks on the main scale, hence
Main Scale division (MSD) = \[\dfrac{{10}}{{250}} = 0.04\]
Fifty divisions of the vernier scale coincide with 15mm= \[\dfrac{{15}}{{10}} = 1.5\]cm of the main scale, where one vernier scale division (VSD) is the distance between two successive marks on the Vernier scale.
VSD= \[\dfrac{{1.5}}{{50}} = 0.03\]
Hence the least count, which is the smallest value that an instrument can measure, will be
Least Count =MSD-LSD
\[
   = 0.04 - 0.03 \\
   = 0.01 \\
 \]
Hence the least count of the instrument will be 0.01cm.

Note:
Students must note that the divisions on the vernier scale are shorter than those on the main scale by 1/25 of the division; if the vernier scale has 25 divisions, the main scale will have 24 divisions of the same length.