The diameter of a wire is measured with a screw gauge having least count `0.01 mm`. Out of the following the one which correctly expresses its diameter is

Options

A. 0.20 cm
B. 0.002 m
C. 2.00 mm
D. 0.2 cm

Answer

To solve the problem of expressing the diameter of a wire measured with a screw gauge having a least count of 0.01 mm, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Least Count**: The least count of the screw gauge is given as 0.01 mm. This means that the smallest measurement that can be accurately read from the screw gauge is 0.01 mm.

2. **Determine the Measurement Format**: Since the least count is 0.01 mm, any measurement of the diameter must be expressed in multiples of this least count. This means that the diameter can be expressed as a value that is a multiple of 0.01 mm.

3. **Analyze the Given Options**: We need to look at the options provided and see which one can be expressed as a multiple of 0.01 mm.

4. **Check Each Option**:
- If we consider option C, which is 2.00 mm:
- To check if this is a multiple of 0.01 mm, we can divide 2.00 mm by 0.01 mm:
\[ \frac{2.00 \text{ mm}}{0.01 \text{ mm}} = 200 \]
- Since 200 is a whole number, 2.00 mm is indeed a multiple of 0.01 mm.

5. **Conclusion**: After checking the options, we find that option C (2.00 mm) is the only one that can be expressed as a multiple of the least count (0.01 mm). Therefore, the correct expression for the diameter of the wire is:
\[ \text{Diameter} = 2.00 \text{ mm} \]

### Final Answer:
The diameter of the wire is correctly expressed as **2.00 mm**.

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