Question

Vernier constant of the Vernier callipers is : (1) least count of Vernier callipers (2) value of 1 division of main scale (3) value of 1 division of vernier scale (4) None of these

Short answer

The correct option is (1) - the least count of Vernier calipers.

Step-by-step solution

- Understanding the Vernier Calipers

Vernier calipers consist of a main scale and a Vernier scale. These two scales help in measuring lengths with high precision.

- Definition of Vernier Constant

The Vernier constant is defined as the difference between one main scale division (MSD) and one Vernier scale division (VSD). It's also known as the least count.

- Determine Option Descriptions

Look at each option to determine its relevance:1. Least count of Vernier calipers2. Value of 1 division of main scale3. Value of 1 division of Vernier scale4. None of these

- Identify the Correct Option

The Vernier constant is indeed the least count of Vernier calipers. Hence, the correct option is (1).

Key concepts

least count

The least count of Vernier calipers is a crucial concept to understand. It defines the smallest length that can be measured accurately with the calipers. The least count is calculated as the difference between one main scale division (MSD) and one Vernier scale division (VSD). Essentially, this allows the Vernier calipers to measure small differences more precisely. When using Vernier calipers, the least count directly impacts how accurately you can read the measurement. If a Vernier caliper has a smaller least count, it means it can measure smaller units accurately, increasing the overall precision of measurements.
For example, if the main scale of the calipers has divisions of 1 mm and the Vernier scale has 10 divisions making up 9 mm, then the least count can be calculated as:
\( \text{Least Count} = 1 \text{ MSD} - (\frac{9 \text{ mm}}{10 \text{ divisions}}) \)
\( = 1 \text{ mm} - 0.9 \text{ mm} = 0.1 \text{ mm} \)
This means the Vernier calipers can measure up to 0.1 mm accurately.

main scale

The main scale on Vernier calipers is the fixed part of the instrument with uniformly spaced divisions. It acts as the primary reference for measurements. The value of one division on the main scale (MSD) is often marked in millimeters (mm) or inches, depending on the calipers.
The main scale provides the coarse measurement of the object being measured, while the Vernier scale adds finer precision. For instance, if each division on the main scale is 1 mm, then you can initially read the measurement to the nearest millimeter on the main scale.
To get an accurate reading:

• Note the value on the main scale just before zero on the Vernier scale.

This value is your coarse measurement, to which you'll add the precise reading from the Vernier scale.

Vernier scale

The Vernier scale is a sliding scale used on Vernier calipers to provide precision measurement. The Vernier scale works in tandem with the main scale and has divisions that are slightly different in length than those on the main scale. Typically, 10 divisions on the Vernier scale correspond to 9 divisions on the main scale.
The Vernier scale helps in fine-tuning the measurement by showing how many divisions past the main scale reading the object extends. Here's how you use it:

• First, read the main scale measurement just to the left of the zero mark of the Vernier scale.
• Next, find the exact line on the Vernier scale that aligns perfectly with any line on the main scale. This alignment helps determine the fractional part of the measurement.

For instance, if the 0.6 mark on the Vernier scale aligns perfectly with a mark on the main scale, this means you add 0.6 mm to the main scale reading for a precise measurement.