A vernier callipers has 20 divisions on the vernier scale which coincide with 19 divisions on the main scale. The least count of the instrument is 0.1 mm. The main scale divisions are of

Options

A. `0.5mm`
B. `1mm`
C. `2mm`
D. `1//4mm`

Answer

To find the main scale division of the vernier calipers, we can follow these steps:

### Step 1: Understand the relationship between the vernier scale and the main scale
Given that 20 divisions on the vernier scale coincide with 19 divisions on the main scale, we can express this relationship mathematically:
\[ 20 \text{ VSD} = 19 \text{ MSD} \]
where VSD is the vernier scale division and MSD is the main scale division.

### Step 2: Calculate one vernier scale division
From the relationship established in Step 1, we can find the value of one vernier scale division:
\[ 1 \text{ VSD} = \frac{19}{20} \text{ MSD} \]

### Step 3: Write the formula for the least count
The least count (LC) of the instrument is given by the formula:
\[ \text{LC} = \text{MSD} - \text{VSD} \]

### Step 4: Substitute the value of VSD into the least count formula
Substituting the expression for VSD from Step 2 into the least count formula:
\[ \text{LC} = \text{MSD} - \left(\frac{19}{20} \text{ MSD}\right) \]
This simplifies to:
\[ \text{LC} = \text{MSD} - \frac{19}{20} \text{ MSD} = \frac{1}{20} \text{ MSD} \]

### Step 5: Use the given least count to find the main scale division
We know from the problem that the least count is 0.1 mm. Therefore, we can set up the equation:
\[ \frac{1}{20} \text{ MSD} = 0.1 \text{ mm} \]

### Step 6: Solve for the main scale division
To find the main scale division (MSD), we multiply both sides of the equation by 20:
\[ \text{MSD} = 20 \times 0.1 \text{ mm} = 2 \text{ mm} \]

### Final Answer
The main scale divisions are of **2 mm**.

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