A screw gauge gives the following reading when used to measure the diameter of a wire. Main scale reading `=0mm`, circular scale reading `=52` divisions. Given that `1mm` on main scale corresponds to `100` divisions of the circular scale. The diameter of the wire from the above data is

Options

A. `0.052cm`
B. `0.026cm`
C. `0.005cm`
D. `0.52cm`

Explanation

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

### Step 1: Determine the Least Count of the Screw Gauge
The least count (LC) is defined as the smallest measurement that can be read on the screw gauge. Given that 1 mm on the main scale corresponds to 100 divisions on the circular scale, we can calculate the least count as follows:

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

### Step 2: Read the Main Scale and Circular Scale
From the problem, we have:
- Main Scale Reading (MSR) = 0 mm
- Circular Scale Reading (CSR) = 52 divisions

### Step 3: Convert Circular Scale Reading to mm
To convert the circular scale reading to mm, we multiply the circular scale reading by the least count:

\[ \text{Circular Scale Reading in mm} = \text{CSR} \times \text{LC} = 52 \times 0.01 \text{ mm} = 0.52 \text{ mm} \]

### Step 4: Calculate the True Reading
The true reading (TR) is calculated by adding the main scale reading to the circular scale reading. Since there is no zero error mentioned, we can assume zero correction is 0.

\[ \text{True Reading (TR)} = \text{MSR} + \text{Circular Scale Reading} = 0 \text{ mm} + 0.52 \text{ mm} = 0.52 \text{ mm} \]

### Step 5: Convert the Diameter to cm (if required)
To convert the diameter from mm to cm:

\[ \text{Diameter in cm} = \frac{0.52 \text{ mm}}{10} = 0.052 \text{ cm} \]

### Final Answer
The diameter of the wire is **0.52 mm** or **0.052 cm**.

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