The pitch of the screw gauge is 1mm and there are 100 divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies 8 divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while `72^(nd)` division on circular scale coincides with the reference line. The radius of the wire is

Options

A. `1.64 mm`
B. `0.82 mm`
C. `1.80 mm`
D. `0.90 mm`

Answer

To solve the problem, we need to determine the radius of the wire using the information provided about the screw gauge.

### Step-by-Step Solution:

1. **Understanding the Screw Gauge**:
- The pitch of the screw gauge is given as 1 mm. This means that for one complete rotation of the screw, the distance moved by the screw is 1 mm.
- There are 100 divisions on the circular scale. Therefore, the least count (LC) of the screw gauge can be calculated as:
\[ \text{Least Count (LC)} = \frac{\text{Pitch}}{\text{Number of divisions on circular scale}} = \frac{1 \text{ mm}}{100} = 0.01 \text{ mm} = 0.001 \text{ cm} \]

2. **Determining Zero Error**:
- When nothing is placed between the jaws, the zero of the circular scale lies 8 divisions below the reference line. This indicates a negative zero error.
- The zero error can be calculated as:
\[ \text{Zero Error} = -8 \times \text{Least Count} = -8 \times 0.01 \text{ mm} = -0.08 \text{ mm} \]

3. **Reading the Measurement with the Wire**:
- When the wire is placed between the jaws, the first linear scale division (1 mm) is visible, and the 72nd division of the circular scale coincides with the reference line.
- The reading on the screw gauge can be calculated as:
\[ \text{Reading} = \text{Main Scale Reading} + \text{Circular Scale Reading} - \text{Zero Error} \]
- The main scale reading is 1 mm (first division), and the circular scale reading is:
\[ \text{Circular Scale Reading} = 72 \times \text{Least Count} = 72 \times 0.01 \text{ mm} = 0.72 \text{ mm} \]
- Now substituting these values into the reading equation:
\[ \text{Reading} = 1 \text{ mm} + 0.72 \text{ mm} - (-0.08 \text{ mm}) = 1 + 0.72 + 0.08 = 1.8 \text{ mm} \]

4. **Calculating the Radius of the Wire**:
- The total reading gives us the diameter of the wire since the screw gauge measures the distance between the jaws, which is equal to the diameter of the wire.
- Therefore, the radius \( r \) of the wire is:
\[ r = \frac{\text{Diameter}}{2} = \frac{1.8 \text{ mm}}{2} = 0.9 \text{ mm} \]

### Final Answer:
The radius of the wire is **0.9 mm**.