Assuming negligible zero error, Find the thickness of the wire,If In a screw gauge, 5 complete rotations of the screw cause if to move a linear distance of `0.25 cm`. There are `100` circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of 4 main scale divisions and 30 circular scale divisions.

Answer

To find the thickness of the wire using the screw gauge, we can follow these steps:

### Step 1: Calculate the distance moved by the screw in one complete rotation
The problem states that 5 complete rotations cause the screw to move a linear distance of 0.25 cm. Therefore, the distance moved by the screw in one rotation can be calculated as follows:

\[ \text{Distance moved in one rotation} = \frac{0.25 \, \text{cm}}{5} = 0.05 \, \text{cm} \]

### Step 2: Calculate the least count of the screw gauge
The least count (LC) of the screw gauge can be calculated using the formula:

\[ \text{Least Count} = \frac{\text{Distance moved in one rotation}}{\text{Number of circular scale divisions}} \]

Given that there are 100 circular scale divisions:

\[ \text{Least Count} = \frac{0.05 \, \text{cm}}{100} = 0.0005 \, \text{cm} \]

### Step 3: Calculate the total reading from the screw gauge
The thickness of the wire is given by the readings on the screw gauge. We have:
- Main Scale Reading (MSR) = 4 main scale divisions
- Circular Scale Reading (CSR) = 30 circular scale divisions

The total reading can be calculated as:

\[ \text{Total Reading} = (\text{MSR} \times \text{Least Count}) + (\text{CSR} \times \text{Least Count}) \]

Substituting the values:

\[ \text{Total Reading} = (4 \times 0.05) + (30 \times 0.0005) \]

Calculating each part:

1. \(4 \times 0.05 = 0.20 \, \text{cm}\)
2. \(30 \times 0.0005 = 0.015 \, \text{cm}\)

Now, adding these two results together:

\[ \text{Total Reading} = 0.20 \, \text{cm} + 0.015 \, \text{cm} = 0.215 \, \text{cm} \]

### Conclusion
The thickness of the wire measured by the screw gauge is:

\[ \text{Thickness of the wire} = 0.215 \, \text{cm} \]

---