One centimetre on the main scale of vernier callipers is divided into ten equal parts. If 20 divisions of vernier scale coincide with 19 small divisions of the main scale then what will be the least count of the callipers.

Explanation

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

### Step 1: Understand the divisions
1 cm on the main scale is divided into 10 equal parts. Therefore, each main scale division (MSD) is:
\[ \text{MSD} = \frac{1 \text{ cm}}{10} = 0.1 \text{ cm} \]

### Step 2: Relate the vernier scale to the main scale
We know that 20 divisions of the vernier scale (VSD) coincide with 19 divisions of the main scale. This means:
\[ 20 \text{ VSD} = 19 \text{ MSD} \]

### Step 3: Calculate the value of one vernier scale division
To find the value of one vernier scale division (VSD), we can express it in terms of the main scale division:
\[ \text{VSD} = \frac{19 \text{ MSD}}{20} = \frac{19}{20} \text{ MSD} \]

### Step 4: Substitute the value of MSD
Now, substituting the value of MSD into the equation:
\[ \text{VSD} = \frac{19}{20} \times 0.1 \text{ cm} = \frac{19 \times 0.1}{20} \text{ cm} = \frac{1.9}{20} \text{ cm} \]

### Step 5: Calculate the least count
The least count (LC) of the vernier calipers is given by the formula:
\[ \text{LC} = \text{MSD} - \text{VSD} \]
Substituting the values we have:
\[ \text{LC} = 0.1 \text{ cm} - \frac{1.9}{20} \text{ cm} \]
To perform the subtraction, we convert 0.1 cm into a fraction:
\[ 0.1 \text{ cm} = \frac{2}{20} \text{ cm} \]
Now we can subtract:
\[ \text{LC} = \frac{2}{20} \text{ cm} - \frac{1.9}{20} \text{ cm} = \frac{2 - 1.9}{20} \text{ cm} = \frac{0.1}{20} \text{ cm} \]
\[ \text{LC} = 0.005 \text{ cm} \]

### Final Answer
The least count of the vernier calipers is:
\[ \text{Least Count} = 0.005 \text{ cm} \]