In a vernier calipers, `1 cm` of the main scale is divided into `20` equal parts. `19` divisions of the main scale coincide with `20` divisions on the vernier scale . Find the least count of the instrument.

Explanation

To find the least count of the vernier calipers, we can follow these steps:

### Step 1: Determine the value of one main scale division (MSD)
Given that 1 cm of the main scale is divided into 20 equal parts, we can calculate the value of one main scale division (MSD) as follows:

\[ \text{MSD} = \frac{1 \text{ cm}}{20} = 0.05 \text{ cm} \]

### Step 2: Determine the value of one vernier scale division (VSD)
It is given that 19 divisions of the main scale coincide with 20 divisions of the vernier scale. Therefore, we can express the value of one vernier scale division (VSD) in terms of the main scale divisions:

\[ \text{VSD} = \frac{19 \text{ MSD}}{20} = \frac{19}{20} \times 0.05 \text{ cm} = 0.0475 \text{ cm} \]

### Step 3: Calculate the least count (LC)
The least count of the vernier calipers is defined as the difference between one main scale division and one vernier scale division:

\[ \text{Least Count} = \text{MSD} - \text{VSD} \]

Substituting the values we found:

\[ \text{Least Count} = 0.05 \text{ cm} - 0.0475 \text{ cm} = 0.0025 \text{ cm} \]

### Conclusion
Thus, the least count of the vernier calipers is:

\[ \text{Least Count} = 0.0025 \text{ cm} \]

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