Question

A screw gauge has pitch \(=0.5\ \text{mm}\) and number of divisions on circular scale \(=50\). Find least count.

• A. \(0.1\ \text{mm}\)
• B. \(0.01\ \text{mm}\)
• C. \(0.001\ \text{mm}\)
• D. \(0.05\ \text{mm}\)

Hint:

For screw gauge: \[ \text{Least Count}=\frac{\text{Pitch}}{\text{Number of circular scale divisions}} \]

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
A screw gauge (micrometer) is an instrument used for measuring the thickness or diameter of small objects with high precision.
Its working is based on the principle of a screw.
The "Pitch" of a screw gauge is the linear distance moved by the screw on the main scale when the circular scale is given one complete rotation.
The "Least Count" is the smallest value that can be measured by the instrument. It is essentially the distance moved by the screw when the circular scale is rotated by exactly one division.
Step 2: Key Formula or Approach:
The formula for the least count (L.C.) of a screw gauge is:
\[ \text{Least Count} = \frac{\text{Pitch of the screw}}{\text{Total number of divisions on the circular scale}} \]
Step 3: Detailed Explanation:
1. Note the given values from the problem:
- Pitch = 0.5 mm.
- Number of divisions (\(n\)) = 50.
2. Apply the values to the formula:
\[ \text{L.C.} = \frac{0.5 \text{ mm}}{50} \]
3. Perform the calculation:
To make the division simpler, you can write 0.5 as \( \frac{1}{2} \):
\[ \text{L.C.} = \frac{1/2}{50} = \frac{1}{100} \text{ mm} \]
\[ \text{L.C.} = 0.01 \text{ mm} \]
4. Unit Check: The result is in mm, which matches the units given in the options.
Step 4: Final Answer:
The least count of the screw gauge is 0.01 mm.
This corresponds to Option (B).