The distance moved by the screw of a screw gauge is `2 mm` in four rotations and there are `50` divisions on its cap. When nothing is put between its jaws, `20th` divisions of circular scale coincides with reference line, and zero of linear scale is hidden from circular scale when two jaws touch each other or zero circular scale is laying above the reference line. When plate is placed between the jaws, main scale reads `2` divisions and circular scale reads `20` divisions. Thickness of plate is.

Options

A. 1.1 mm
B. 1.2 mm
C. 1.4 mm
D. 1.5 mm

Explanation

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

### Step 1: Calculate the Pitch of the Screw Gauge
The pitch of the screw gauge is defined as the distance moved by the screw for one complete rotation. Given that the screw moves `2 mm` in `4 rotations`, we can calculate the pitch as follows:

\[ \text{Pitch} = \frac{\text{Distance moved}}{\text{Number of rotations}} = \frac{2 \text{ mm}}{4} = 0.5 \text{ mm} \]

### Step 2: Calculate the Least Count of the Screw Gauge
The least count (LC) of the screw gauge is given by the formula:

\[ \text{Least Count} = \frac{\text{Pitch}}{\text{Number of divisions on circular scale}} = \frac{0.5 \text{ mm}}{50} = 0.01 \text{ mm} = \frac{1}{100} \text{ mm} \]

### Step 3: Determine the Error in the Screw Gauge
When nothing is placed between the jaws, the `20th division` of the circular scale coincides with the reference line, and the `0` of the linear scale is above the reference line. This indicates a negative error. The number of divisions between `0` and `20` is:

\[ \text{Number of divisions} = 50 - 20 = 30 \]

The error can be calculated as:

\[ \text{Error} = \text{Number of divisions} \times \text{Least Count} = 30 \times \frac{1}{100} \text{ mm} = 0.3 \text{ mm} \]

Since this is a negative error, we write it as:

\[ \text{Error} = -0.3 \text{ mm} \]

### Step 4: Calculate the Observed Thickness of the Plate
When the plate is placed between the jaws, the main scale reading (MSR) is `2 divisions` and the circular scale reading (CSD) is `20 divisions`. The observed thickness (L) can be calculated as:

\[ \text{Observed Thickness} = \text{MSR} \times \text{Pitch} + \text{CSD} \times \text{Least Count} \]

Substituting the values:

\[ \text{Observed Thickness} = 2 \times 0.5 \text{ mm} + 20 \times \frac{1}{100} \text{ mm} = 1 \text{ mm} + 0.2 \text{ mm} = 1.2 \text{ mm} \]

### Step 5: Calculate the Actual Thickness of the Plate
The actual thickness of the plate is given by:

\[ \text{Actual Thickness} = \text{Observed Thickness} - \text{Error} \]

Substituting the values:

\[ \text{Actual Thickness} = 1.2 \text{ mm} - (-0.3 \text{ mm}) = 1.2 \text{ mm} + 0.3 \text{ mm} = 1.5 \text{ mm} \]

### Final Answer
The thickness of the plate is:

\[ \text{Thickness of the plate} = 1.5 \text{ mm} \]