The meehanism behind nut and bolt arrangement also works for screw gauge.
In case of nut and bolt mechanism, with rotation of bolt, it has translational movement also. In one complete rotation of bolt, tip of bolt moves by a linear distance equal to linear distance between two consecutive threads on the screw, known as pitch in case of screw gauge, the circular scale is divided in several parths. The ratio of pitch and total number of divisions on circular scale is known as least count. Spherometer is a device used to measure very small distances such as radius of curvature and thicness of thin plate. The screw gauge can be used to meaure diameter of a spherical sample. A screw gauge has 100 divisions on head scale and in 8 rotations distance covered is 8 mm.
Least count of given screw gauge is

Options

A. 0.08 mm
B. 0.02 mm
C. 0.01 mm
D. 1 mm

Answer

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

### Step-by-Step Solution:

1. **Understand the Concept of Pitch**:
The pitch of a screw gauge is defined as the distance moved by the screw in one complete rotation. In this case, we know that in 8 rotations, the distance covered is 8 mm.

2. **Calculate the Pitch**:
Since the distance covered in 8 rotations is 8 mm, we can find the pitch (distance moved in one rotation) as follows:
\[ \text{Pitch} = \frac{\text{Total distance}}{\text{Number of rotations}} = \frac{8 \text{ mm}}{8} = 1 \text{ mm} \]

3. **Identify the Number of Divisions on Circular Scale**:
The problem states that there are 100 divisions on the circular scale of the screw gauge.

4. **Calculate the Least Count**:
The least count (LC) of the screw gauge is given by the formula:
\[ \text{Least Count} = \frac{\text{Pitch}}{\text{Number of divisions on circular scale}} \]
Substituting the values we have:
\[ \text{Least Count} = \frac{1 \text{ mm}}{100} = 0.01 \text{ mm} \]

5. **Conclusion**:
Therefore, the least count of the given screw gauge is \(0.01 \text{ mm}\).

### Final Answer:
The least count of the given screw gauge is \(0.01 \text{ mm}\).

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