In a vernier callipers, smallest division on the main scale is `1mm`, while the vernier scale have `20` divisions. When fixed jaw touches with movable jaw, zero of vernier scale lies on the right of the zero of the main scale and `15th` division of vernier scale coincides with any division of main scale. What is the type of zero error and its value?

Options

A. positive, `0.75 mm`
B. negative, `0.75 mm`
C. positive, `0.15 mm`
D. negative, `0.15mm`

Answer

To solve the problem regarding the vernier calipers and determine the type of zero error and its value, we can follow these steps:

### Step 1: Understand the Setup
We have a vernier caliper where:
- The smallest division on the main scale (MSD) is 1 mm.
- The vernier scale (VS) has 20 divisions.

### Step 2: Calculate the Least Count (LC)
The least count of the vernier calipers can be calculated using the formula:
\[ \text{Least Count (LC)} = \text{Value of 1 MSD} - \text{Value of 1 VSD} \]
Where VSD is the value of one division on the vernier scale. Since the vernier scale has 20 divisions that equal 1 mm:
\[ \text{Value of 1 VSD} = \frac{1 \text{ mm}}{20} = 0.05 \text{ mm} \]
Now, substituting the values:
\[ \text{LC} = 1 \text{ mm} - 0.05 \text{ mm} = 0.95 \text{ mm} \]

### Step 3: Identify the Zero Error
According to the problem, when the fixed jaw touches the movable jaw, the zero of the vernier scale lies to the right of the zero of the main scale. This indicates a positive zero error.

### Step 4: Determine the Zero Error Value
The zero error can be calculated based on the division of the vernier scale that coincides with the main scale. The 15th division of the vernier scale coincides with a division of the main scale. Therefore, the zero error can be calculated as:
\[ \text{Zero Error} = \text{(Vernier scale division that coincides)} \times \text{Least Count} \]
Substituting the values:
\[ \text{Zero Error} = 15 \times 0.05 \text{ mm} = 0.75 \text{ mm} \]

### Final Answer
The type of zero error is **positive zero error**, and its value is **0.75 mm**.

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