Least count of screw gauge is defined as.

Options

A. `(a) ("distance moved by thimble on main scale")/("number of rotation of thimble")`
B. `(b)("pitch of the screw") /(" number of divisions on circular scale")`
C. `(c)("number of rotation of thimble") /(" number of circular scale divisions")`
D. (d)None of the above.

Answer

To define the least count of a screw gauge, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Screw Gauge**:
A screw gauge (or micrometer screw gauge) is an instrument used to measure small lengths with high precision. It consists of a screw and a circular scale.

2. **Identifying Key Terms**:
- **Pitch of the Screw**: This is the distance moved by the thimble (the rotating part of the screw gauge) in one complete rotation.
- **Circular Scale Divisions**: This refers to the number of divisions marked on the circular scale of the screw gauge.

3. **Defining Least Count**:
The least count of the screw gauge is defined as the smallest measurement that can be accurately read with the instrument. It is calculated by the formula:
\[ \text{Least Count} = \frac{\text{Pitch of the Screw}}{\text{Number of Circular Scale Divisions}} \]

4. **Evaluating Options**:
- **Option A**: Incorrect, as it does not relate the pitch to the circular scale divisions correctly.
- **Option B**: Correct, as it accurately describes the least count using the pitch and the number of divisions.
- **Option C**: Incorrect, as it results in a dimensionless quantity, which does not make sense for a measurement of length.

5. **Conclusion**:
Therefore, the least count of a screw gauge is defined as the pitch of the screw divided by the number of divisions on the circular scale.