The pitch of a screw gauge is `1 mm` and there are `50` divisions on its cap. When nothing is put in between the studs, `44th` divisions of the circular scale coincides with the reference line and the line and the zero of the main scale is not visible or zero of circular scale is lying above the reference line. When a glass plate is placed between the studs, the main scale reads three divisions and the circular scale reads thre divisions and the circular scale reads `26` divisions. Calculate the thickness of the plate.

Explanation

To calculate the thickness of the glass plate using the screw gauge, we can follow these steps:

### Step 1: Calculate the Least Count of the Screw Gauge
The least count (LC) is calculated using the formula:
\[ \text{Least Count} = \frac{\text{Pitch}}{\text{Number of divisions on circular scale}} \]

Given:
- Pitch = 1 mm
- Number of divisions on circular scale = 50

\[ \text{Least Count} = \frac{1 \text{ mm}}{50} = 0.02 \text{ mm} \]

### Step 2: Determine the Error in the Screw Gauge
When nothing is placed between the studs, the 44th division of the circular scale coincides with the reference line. Since the zero of the main scale is not visible, we need to calculate the error.

The error can be calculated as:
\[ \text{Error} = \left( \text{Number of divisions on circular scale} - \text{Division coinciding with reference line} \right) \times \text{Least Count} \]

Substituting the values:
\[ \text{Error} = (50 - 44) \times 0.02 \text{ mm} = 6 \times 0.02 \text{ mm} = 0.12 \text{ mm} \]
Since the zero of the circular scale is above the reference line, the error is negative:
\[ \text{Error} = -0.12 \text{ mm} \]

### Step 3: Read the Measurements with the Glass Plate
When the glass plate is placed between the studs:
- Main scale reading (MSR) = 3 divisions
- Circular scale reading (CSR) = 26 divisions

### Step 4: Calculate the Observed Value
The thickness of the plate can be calculated using the formula:
\[ \text{Thickness} = \text{MSR} + (\text{CSR} \times \text{Least Count}) - \text{Error} \]

Substituting the values:
- MSR = 3 divisions = 3 mm (since pitch is 1 mm)
- CSR = 26 divisions
- Least Count = 0.02 mm
- Error = -0.12 mm

Calculating:
\[ \text{Thickness} = 3 \text{ mm} + (26 \times 0.02 \text{ mm}) - (-0.12 \text{ mm}) \]
\[ \text{Thickness} = 3 \text{ mm} + 0.52 \text{ mm} + 0.12 \text{ mm} \]
\[ \text{Thickness} = 3 \text{ mm} + 0.52 \text{ mm} + 0.12 \text{ mm} = 3.64 \text{ mm} \]

### Final Answer
The thickness of the glass plate is **3.64 mm**.

---