Animated Solution for Physics - Physics and Measurement: A vernier calipers has $1\text{ mm}$ marks on the main scale. It has $20$ equal divisions on the vernier scale which match with $16$ main scale divisions. For this vernier calipers, the least count is

Imagine you are trying to measure the thickness of a small coin. A regular ruler might tell you it's between $1\text{ mm}$ and $2\text{ mm}$, but it can't give you the exact decimal value. This is where the brilliant invention of the Vernier Caliper comes in. It uses two scales sliding past each other to give you highly precise measurements.

In our problem, we are given a specific vernier caliper. The main scale is just like a regular ruler, with marks every $1\text{ mm}$. This means that one Main Scale Division (MSD) is exactly $1\text{ mm}$.

Now, let's look at the vernier scale. The problem states a crucial matching condition: $20$ equal divisions on the vernier scale perfectly align with $16$ divisions on the main scale. This is the key to unlocking the precision of the instrument.

From the matching condition, we can determine the exact length of a single Vernier Scale Division (VSD). If $20\text{ VSD}$ cover the same distance as $16\text{ MSD}$, then:

Dividing both sides by $20$, we find the length of one VSD:

Since we know that $1\text{ MSD}=1\text{ mm}$, we can substitute this value in:

So, each little mark on the vernier scale is $0.8\text{ mm}$ apart.

The Least Count (LC) of a vernier caliper is the smallest possible measurement it can accurately record. It is defined as the difference in length between one main scale division and one vernier scale division.

Let's plug in the values we've found:

And there we have it! The least count of this specific vernier caliper is $0.2\text{ mm}$. This means the instrument can measure lengths with a precision of $0.2\text{ mm}$.