The circular scale head of a screw gauge is divided into 200 divisions and move 1 mm ahead in one revolution. The diameter of the wire, when the pitch scale reading shows 6mm (when the wire is firmly held between the studes) and `45^(th)` division on circular scale coincides with the reference line.

Options

A. 6.220 mm
B. 6.225 mm
C. 6.175 mm
D. 6.375 mm

Answer

To find the diameter of the wire using the screw gauge, we will follow these steps:

### Step 1: Understand the given information
- The screw gauge has a circular scale divided into 200 divisions.
- One complete revolution of the screw gauge moves the scale by 1 mm.
- The main scale reading (MSR) is 6 mm.
- The circular scale reading (CSR) is the 45th division.

### Step 2: Calculate the Least Count (LC)
The least count of the screw gauge can be calculated using the formula:
\[ \text{Least Count (LC)} = \frac{\text{Pitch}}{\text{Number of divisions in circular scale}} \]
Where:
- Pitch = 1 mm (the distance moved in one complete revolution)
- Number of divisions in circular scale = 200

Substituting the values:
\[ \text{LC} = \frac{1 \text{ mm}}{200} = 0.005 \text{ mm} \]

### Step 3: Calculate the total reading
The total reading (diameter of the wire) can be calculated using the formula:
\[ \text{Diameter} = \text{Main Scale Reading (MSR)} + \left(\text{Circular Scale Reading (CSR)} \times \text{Least Count (LC)}\right) \]
Where:
- MSR = 6 mm
- CSR = 45 divisions
- LC = 0.005 mm

Substituting the values:
\[ \text{Diameter} = 6 \text{ mm} + (45 \times 0.005 \text{ mm}) \]
Calculating the second term:
\[ 45 \times 0.005 = 0.225 \text{ mm} \]
Now, substituting back into the diameter formula:
\[ \text{Diameter} = 6 \text{ mm} + 0.225 \text{ mm} = 6.225 \text{ mm} \]

### Final Answer
The diameter of the wire is **6.225 mm**.

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