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 relationship between the divisions of the scales
According to the problem, 20 divisions of the vernier scale (VSD) coincide with 19 divisions of the main scale (MSD). This can be expressed mathematically as:
\[ 20 \, \text{VSD} = 19 \, \text{MSD} \]

### Step 2: Calculate the value of one Vernier Scale Division (VSD)
From the above relationship, we can find the value of one Vernier Scale Division:
\[ \text{VSD} = \frac{19}{20} \, \text{MSD} \]

### Step 3: Determine the value of one Main Scale Division (MSD)
Since 1 cm on the main scale is divided into 10 equal parts, the value of one Main Scale Division (MSD) is:
\[ \text{MSD} = \frac{1 \, \text{cm}}{10} = 0.1 \, \text{cm} \]

### Step 4: Substitute the value of MSD into the equation for VSD
Now, substituting the value of MSD into the equation for VSD:
\[ \text{VSD} = \frac{19}{20} \times 0.1 \, \text{cm} \]
\[ \text{VSD} = \frac{19 \times 0.1}{20} \, \text{cm} = \frac{1.9}{20} \, \text{cm} = 0.095 \, \text{cm} \]

### Step 5: Calculate the Least Count (LC)
The least count of the vernier calipers is given by the difference between one Main Scale Division (MSD) and one Vernier Scale Division (VSD):
\[ \text{LC} = \text{MSD} - \text{VSD} \]
Substituting the values we have:
\[ \text{LC} = 0.1 \, \text{cm} - 0.095 \, \text{cm} \]
\[ \text{LC} = 0.005 \, \text{cm} \]

### Final Answer
Thus, the least count of the vernier calipers is:
\[ \text{LC} = 0.005 \, \text{cm} \]

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