Two full turns of the circular scale of a screw gauge cover a distance of `1mm` on its main scale. The total number of divisions on the circular scale is `50`. Further, it is found that the screw gauge has a zero error of `- 0.03mm`. While main scale reading of `3mm` and the number of circular scale divisions in line with the main scale as `35`. the dimeter of the wire is

Options

A. 3.32 mm
B. 3.73 mm
C. 3.67 mm
D. 3.38 mm

Answer

To find the diameter of the wire using the given parameters, we will follow these steps:

### Step 1: Determine the Pitch of the Screw Gauge
The pitch of the screw gauge is defined as the distance moved by the screw for one complete turn of the circular scale.

Given that:
- Two full turns cover a distance of 1 mm.

Therefore, the distance covered in one turn (pitch) is:
\[ \text{Pitch} = \frac{1 \text{ mm}}{2} = 0.5 \text{ mm} \]

### Step 2: Calculate the Least Count of the Screw Gauge
The least count (LC) of the screw gauge can be calculated using the formula:
\[ \text{Least Count} = \frac{\text{Pitch}}{\text{Total Number of Divisions}} \]

Given that:
- Total number of divisions on the circular scale = 50

Substituting the values:
\[ \text{Least Count} = \frac{0.5 \text{ mm}}{50} = 0.01 \text{ mm} \]

### Step 3: Calculate the Observed Reading
The observed reading of the screw gauge can be calculated using the formula:
\[ \text{Reading} = \text{Main Scale Reading} + (\text{Circular Scale Reading} \times \text{Least Count}) - \text{Zero Error} \]

Given:
- Main Scale Reading (MSR) = 3 mm
- Circular Scale Reading (CSR) = 35 divisions
- Zero Error = -0.03 mm

Substituting the values:
\[ \text{Reading} = 3 \text{ mm} + (35 \times 0.01 \text{ mm}) - (-0.03 \text{ mm}) \]
\[ \text{Reading} = 3 \text{ mm} + 0.35 \text{ mm} + 0.03 \text{ mm} \]
\[ \text{Reading} = 3.68 \text{ mm} \]

### Step 4: Final Calculation of the Diameter
The diameter of the wire is equal to the observed reading calculated above:
\[ \text{Diameter of the wire} = 3.68 \text{ mm} \]

### Final Answer
The diameter of the wire is **3.68 mm**.

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