The pitch of a screw gauge is 1 mm and there are 100 divisions on circular scale. When the two studs of the screw gauge are touching each other, the `32^(nd)` division of the circulasr scale coincides with the reference line / base line / index line on the pitch scale. When a glass plate is placed in between the studs firmly, the pitch scale reads 4 divisions and the circular scale reads 16 divisions
The thickness of glass plate is

Options

A. 3.84 cm
B. 4.48 mm
C. 3.84 mm
D. 3.84 mm

Answer

To find the thickness of the glass plate using the screw gauge, we will follow these steps:

### Step 1: Determine the Least Count of the Screw Gauge
The least count (LC) of a screw gauge 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 = 100

Substituting the values:

\[ \text{Least Count} = \frac{1 \text{ mm}}{100} = 0.01 \text{ mm} \]

### Step 2: Calculate the Error in the Screw Gauge
The error is determined by the division of the circular scale that coincides with the reference line when the studs are touching.

Given:
- Error division = 32

The error can be calculated as:

\[ \text{Error} = \text{Error Division} \times \text{Least Count} \]

Substituting the values:

\[ \text{Error} = 32 \times 0.01 \text{ mm} = 0.32 \text{ mm} \]

### Step 3: Calculate the Thickness of the Glass Plate
The thickness of the glass plate can be calculated using the formula:

\[ \text{Thickness} = \text{Main Scale Reading} + (\text{Circular Scale Reading} \times \text{Least Count}) - \text{Error} \]

Given:
- Main Scale Reading = 4 divisions
- Circular Scale Reading = 16 divisions

Substituting the values:

\[ \text{Thickness} = 4 + (16 \times 0.01) - 0.32 \]

Calculating it step-by-step:

1. Calculate \(16 \times 0.01 = 0.16\)
2. Now substitute back into the equation:

\[ \text{Thickness} = 4 + 0.16 - 0.32 \]

3. Simplifying gives:

\[ \text{Thickness} = 4 + 0.16 - 0.32 = 4 - 0.16 = 3.84 \text{ mm} \]

### Final Answer
The thickness of the glass plate is **3.84 mm**.

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