Today, I'd like to show to you, the best way to find find Least Count of a vernier-caliper
I will try to explain the concept first & then give a few Examples about finding Least Count for Ruler, Vernier Calipers.
THE CONCEPT
Now, what is Least Count?
Least Count tells you the minimum reading or value that can be measured with a measuring tool or device.Generally, simply multiplying Least Count with the number of divisions (like in ruler) or fraction of divisions (like in Vernier Calipers), we get our answer in the units specified. For Example, 21 divisions in a Ruler would mean 2.1 cm or 21 mm. Least count of a ruler is 0.1 cm or 1 mm (we'll understand how to find it, later in this article).
HOW TO FIND LEAST COUNT
I've seen many people confused about how to find Least Count. The method used by them might be slightly different, tough to remember, so even if they understand it once, the next time they try to do the same, they forget about it, which is not good.
The way I like to make it understandable is related to the definition of Least Count itself. Remember, Least Count gives you the minimum value that can be measured by by the instrument/device/tool. So considering that, Least Count will be:
You can take any number of divisions for finding Least Count, but those have to be the smallest ones. Let us take "n" small divisions.
Value measured in "n" divisions
LC=
n
We'll use the same concept here to find the least count of Ruler, Vernier Calipers although things might change a little in case of Vernier Calipers. I recommend to go through the examples below to understand properly.
Also we'll talk a little about the importance or Physical significance of Least Count, in case of a Ruler.
THE RULER
So for a ruler, that is, the scale, we use in daily life, we can find the Least Count, by the definition formula only, which we did.
Let us take 20 divisions for it (the value of "n". We know that a ruler measures 20 mm or 2 cm, 20 divisions.
Value measured in 20 divisions
LC=
20
= 2 cm/20 = 0.1 cm
Therefore Least Count of a Ruler comes out to be 0.1 cm or 1 mm. Remember, you could even take other values like { 1 cm / 10 }.
Now what is the importance of this value (0.1 cm)?
While calculating, we used 20 divisions. Now 10, 20, 30, 40, etc. are numbers that can be easily dealt with practically, rather than numbers like 13, 17, 27, etc.
What if you wanna calculate the value measured by 23 divisions of a ruler? Here Least Count becomes handy. You can simply multiply 23 with 0.1 cm (the Least Count) & get the answer 2.3 cm.
Therefore, 2.3 cm is the value measured by 23 divisions of a Ruler.
THE VERNIER CALIPERS
Now, Vernier Calipers, is similar to ruler, but a little more complex and can give more specific results. The accuracy of Vernier Calipers is much more than ruler, as the former can give results upto two decimal places (in case of centimeters), whereas the Ruler can only give upto 1.
Now let's talk about what's the Least Count of Vernier Calipers and how to find it.
In case of ruler, there was only 1 scale which gave us the readings, But in Vernier Calipers, there are 2 scales, called "The Main Scale" & "The Vernier Scale". The Main Scale is similar to the Ruler we use, therefore "Main Scale" does the work of providing the results upto the first Decimal Place. (in centimetres)
Consider the Ruler, take the smallest division in it 0.1 cm. Now if we draw 10 more smaller divisions in that, theoretically those will give the second decimal Place.
But is that feasible practically? Of-course not! 0.1 cm (1 mm) is already very small and putting 10 more lines in that would be outrageous. So to do that, Vernier Scale is used. "Vernier Scale" can be considered as the magnified form of those small 10 lines that we were to draw in 0.1 cm of ruler.
So, the above should explain the concept of Vernier Calipers to you. Let's come back to find the Least Count of Vernier Calipers.
In addition to simply finding the minimum value (Least Count) given by Main Scale (ruler), we have to consider the Vernier Scale too (the magnified version of the smaller lines that we were to draw in the 0.1 cm of Ruler). What we'll do is first find the Least Count of the Main Scale and then move onto the Vernier Scale to solve our issue step by step.
The Main Scale (same as Ruler) will give the smallest Reading or Least Count of 0.1 cm, as in case of the Ruler. Next, the formula would be the same:
Value measured in "n" divisions
LC=
n
where "n" are the SMALLEST DIVISIONS. Now I want you to imagine Vernier Scale as the smaller lines in 0.1 cm of the Ruler (Main Scale). What would you consider "n" to be? The smallest lines we've imagined, OR the smaller lines of an actual Ruler (without Vernier Scale). Of-course the first choice is correct. Since "n" are the SMALLEST DIVISIONS, we have to take up the imagined lines, which are drawn in the 0.1 cm gap.
10 are drawn in 0.1 cm gap, 20 in 0.2 cm gap & 30 in 0.3 cm gap. These give the corresponding values of "n" and values measured by n.
So you can take any of them. If you're writing in Exam I'll always recommend you to take up the first one in the series, so the Examiner doesn't get confused. So considering this, we'll take the first one:
n = 10 &
Value measured in 10 (smallest divisions, n) = 0.1 cm.
Correspondingly, The Least Count:
Value measured in 10 divisions (smallest)
LC=
10
0.1 cm
=
10
which turns out to be 0.01 cm. Voila! it's the Least Count of Vernier Calipers. As a special case, the Least Count of a general Vernier Calipers (done above) is also called Vernier Constant.
I hope you got this! This Imagining concept will help you understand the Least Count a lot. It'll help you better know other devices also.
EXERCISE ON VERNIER CALIPERS
So, we've so far found the Least Count of a general Vernier Calipers. Let us exercise the same Imagining Concept on a different Vernier Calipers, having Least Count 0.002 cm, a lot more accurate. This accurate device has been shown in the image below:
Value measured in "n" divisions
LC=
n
Remember, Vernier Scale gives the smallest divisions "n", not the Main Scale. So Imagine the smaller 0.1 cm of the Main Scale being divided into 50 more divisions, such that 0.1 cm gap makes 50 smallest divisions, 0.2 cm makes 100, 0.3 cm gap makes 150, .... So:
Value measured in 50 divisions (smallest)
LC=
50
LC=
50
0.1 cm
=
50
Hope it will help you. thank you.
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