A screw gauge advances by 3mm in 6 rotations. There are 50 divisions on circular scale. Find least count of screw gauge

Options

A. `0.002` cm
B. `0.001` cm
C. `0.1`cm
D. `0.02` cm

Explanation

To find the least count of 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 in one complete rotation.

Given:
- The screw gauge advances by 3 mm in 6 rotations.

To find the pitch (P):
\[ P = \frac{\text{Total advancement}}{\text{Number of rotations}} \]
\[ P = \frac{3 \text{ mm}}{6} = 0.5 \text{ mm} \]

### Step 2: Determine the Least Count
The least count (LC) of the screw gauge is calculated using the formula:
\[ \text{Least Count} = \frac{\text{Pitch}}{\text{Number of divisions on the circular scale}} \]

Given:
- Pitch = 0.5 mm
- Number of divisions on the circular scale = 50

Now, substituting the values:
\[ \text{Least Count} = \frac{0.5 \text{ mm}}{50} \]
\[ \text{Least Count} = 0.01 \text{ mm} \]

### Step 3: Convert the Least Count to Centimeters
To express the least count in centimeters:
\[ \text{Least Count in cm} = 0.01 \text{ mm} \times \frac{1 \text{ cm}}{10 \text{ mm}} = 0.001 \text{ cm} \]

### Conclusion
The least count of the screw gauge is:
\[ \text{Least Count} = 0.001 \text{ cm} \]