Question

If in a vernier callipers 10 VSD coincides with 8 MSD then the least count of varnier calliper is

Answer 1

How much we know about the Vernier calipers?
Measurement is a fundamental part of all scientific experiments, including Physics. At one extreme, our vast universe extends this measuring exercise to light-years, the distances so vast that we cannot see them from our eyes. On the other extreme of the smallest distances, new discoveries are pushing it down to femto-meter (10-15 m) or even less. These distances are so small that we cannot see them from our eyes. At every 1 - 2 order of magnitude change in distance, our instruments to measure the distances accurately can differ. When the distances, we want to measure, are in the range of 10-2 mm to 1 mm, we use Vernier Calipers and Screw Gauge for precise measurement. In this article, we are going to focus on these measuring instruments only.

In class 11th Physics lab, we were trained to answer the following questions:

How to find the Least Count (LC) or Vernier Constant?
How to read Main Scale Reading (MSR) and Vernier Scale Reading (VSR)?
How to find the zero error?
How to use the above data to get the final measurement?
Answers to these how to questions kept us content for 22 years. But this was not adequate to solve the IIT JEE 2016 problem. We needed to figure out some more interesting why questions like:

Why least count is given by
LC = Value of 1 main scale division
------------------------------------
Total number of divisions on Vernier scale
Why the measured value is given by
Observed Value = MSR + LC × VSR
Why the zero error is subtracted from the observed value i.e.,
True Value = Observed Value - Zero Error
Let us start our journey with a Vernier calipers without zero error. When two jaws are closed, 0th mark on the Vernier scale is aligned with the 0th mark on the main scale as shown in the figure 1. Also note that 10th mark on Vernier scale coincides with the 9th mark on main scale.

One main scale division (MSD) is the distance between two successive marks on the main scale. It is given in the figure 1 that 1 MSD is equal to 1mm. One Vernier scale division (VSD) is the distance between two successive marks on the Vernier scale. It is given that 10VSD = 9MSD. Thus, 1VSD = (9∕10)MSD = (9∕10)1mm = 0.9mm i.e., distance between two successive marks on the Vernier scale is 0.9mm.



Figure 1: Vernier calipers with no zero error

Answer 2

Answer:0.2mm

Step-by-step explanation:

The length of one VSD=8/10=0.8mm

The least count of the instrument is the difference between the length of one MSD and length of one VSD

The length of inebriated MSD=1mm

Therefore,

The least count=1-0.8=0.2mm