The pitch of a micrometer screw gauge is 1 mm and the circular scale has 100 divisions. When there is nothing between the jaws, the zero of the circular scale is 8 divisions below the main scale. When a wire is put between the jaws, the 1st division of main scale is visible and 72nd division of circular scale coincides with main scale. The radius of wire is?

Options

A. 1.8mm
B. 0.9mm
C. 1.64mm
D. 0.82mm

Answer

To solve the problem step by step, we will follow the given information about the micrometer screw gauge and calculate the radius of the wire.

### Step 1: Calculate the Least Count (LC)
The least count of a micrometer screw gauge is given by 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

So, we calculate:
\[ \text{Least Count} = \frac{1 \text{ mm}}{100} = 0.01 \text{ mm} \]

### Step 2: Determine the Zero Error
The zero error is the reading when there is nothing between the jaws. It is given that the zero of the circular scale is 8 divisions below the main scale. Therefore, the zero error can be calculated as:
\[ \text{Zero Error} = -8 \times \text{Least Count} = -8 \times 0.01 \text{ mm} = -0.08 \text{ mm} \]

### Step 3: Calculate the Reading with the Wire
When the wire is placed between the jaws, the following readings are noted:
- The first division of the main scale is visible (1 mm).
- The 72nd division of the circular scale coincides with the main scale.

The reading can be calculated as:
\[ \text{Reading} = \text{Main Scale Reading} + \text{Circular Scale Reading} \]
Where:
- Main Scale Reading = 1 mm
- Circular Scale Reading = 72 divisions × Least Count = 72 × 0.01 mm = 0.72 mm

Thus, the total reading is:
\[ \text{Total Reading} = 1 \text{ mm} + 0.72 \text{ mm} = 1.72 \text{ mm} \]

### Step 4: Adjust for Zero Error
To find the correct measurement of the diameter of the wire, we need to adjust for the zero error:
\[ \text{Corrected Reading} = \text{Total Reading} + \text{Zero Error} \]
Substituting the values:
\[ \text{Corrected Reading} = 1.72 \text{ mm} - 0.08 \text{ mm} = 1.64 \text{ mm} \]

### Step 5: Calculate the Radius of the Wire
The corrected reading gives us the diameter of the wire (2R):
\[ 2R = 1.64 \text{ mm} \]
To find the radius (R):
\[ R = \frac{1.64 \text{ mm}}{2} = 0.82 \text{ mm} \]

### Final Answer
The radius of the wire is:
\[ \boxed{0.82 \text{ mm}} \]