Number of Division of the Main Scale equal to 8 divisions of the Extended Vernier

To calculate the number of divisions on the main scale that is equal to 8 divisions on the extended vernier, we need to understand the concept of a vernier scale and how it is used for precise measurements.

Vernier Scale
A vernier scale is a supplemental scale used in precision instruments, such as calipers and micrometers, to improve the accuracy of measurements. It consists of a main scale and an extended vernier scale, which has a smaller division compared to the main scale.

Understanding the Vernier Scale
The main scale is divided into equal divisions, and each division is further divided into a number of smaller divisions. The extended vernier scale is also divided into equal divisions, but the number of divisions is slightly different from the main scale.

Principle of Vernier Scale
The principle behind the vernier scale is that when the zero points of both the main scale and the vernier scale are aligned, the divisions on the vernier scale will not perfectly align with the divisions on the main scale. However, by sliding the vernier scale, the divisions on it can be aligned with the divisions on the main scale.

Calculating the Number of Divisions
To determine the number of divisions on the main scale that is equal to 8 divisions on the extended vernier, we need to find the difference between the smallest division on the main scale and the smallest division on the vernier scale.

Let's assume that the smallest division on the main scale is equal to "x" units, and the smallest division on the vernier scale is equal to "y" units. The difference between the two divisions is given by:

Difference = x - y

Now, since we want to find the number of divisions on the main scale that is equal to 8 divisions on the vernier scale, we can set up the following equation:

8y = Difference

Solving this equation will give us the value of "y", which represents the smallest division on the vernier scale.

Once we have the value of "y", we can calculate the number of divisions on the main scale that is equal to 8 divisions on the vernier scale by dividing the difference between two adjacent divisions on the main scale by "y".

Number of Divisions = Difference / y

In this case, the answer is given as 15, which means there are 15 divisions on the main scale that is equal to 8 divisions on the extended vernier.

15