A screw gauge has 200 equal divisions marked along the circumference of the disc and one full rotation of the disc advances on the main scale by 0.05 cm. The least count of screw gauge is

Options

A. `2.5xx10^(-4)cm`
B. `2.5xx10^(-3)cm`
C. `6.25xx10^(-4)cm`
D. `6.25xx10^(-3)cm`

Explanation

To find the least count of the screw gauge, we will follow these steps:

### Step 1: Understand the Definitions
- **Pitch**: The distance moved by the screw gauge on the main scale for one complete rotation of the circular scale. In this case, it is given as 0.05 cm.
- **Number of Divisions on Circular Scale (N)**: The total number of equal divisions marked on the circular scale. Here, it is 200.

### Step 2: Use the Formula for Least Count
The least count (LC) of a screw gauge can be calculated using the formula:
\[ \text{Least Count (LC)} = \frac{\text{Pitch}}{\text{Number of Divisions on Circular Scale (N)}} \]

### Step 3: Substitute the Values
We have:
- Pitch = 0.05 cm
- N = 200

Substituting these values into the formula:
\[ \text{LC} = \frac{0.05 \, \text{cm}}{200} \]

### Step 4: Perform the Calculation
Calculating the least count:
\[ \text{LC} = \frac{0.05}{200} = 0.00025 \, \text{cm} \]

### Step 5: Convert to Scientific Notation
To express the least count in scientific notation:
\[ 0.00025 \, \text{cm} = 2.5 \times 10^{-4} \, \text{cm} \]

### Conclusion
Thus, the least count of the screw gauge is:
\[ \text{Least Count} = 2.5 \times 10^{-4} \, \text{cm} \]

### Final Answer
The least count of the screw gauge is \( 2.5 \times 10^{-4} \, \text{cm} \).

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