The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure 5 $\mathrm{\mu }$m diameter of the wire will be

The least count of screw gauge is a critical parameter for measuring very small dimensions accurately. In this problem, we need to determine the minimum number of divisions required on the circular scale to measure a diameter of 5 µm using a screw gauge.

Given Data:

• Least count of the main scale = 1 mm
• Diameter to measure = 5 µm

Step-by-Step Calculation:

1. Understanding the Pitch

The pitch of the screw gauge is defined as the distance moved by the screw per complete rotation. Since the least count of the main scale is given as 1 mm, the pitch is:

Pitch = 1 mm

2. Formula for Least Count of Screw Gauge

The least count of screw gauge (L.C.) is calculated using the formula:

Least Count (L.C.) = Pitch / Number of Divisions on Circular Scale

3. Finding the Required Number of Divisions

To measure a diameter of 5 µm, the least count of screw gauge should be:

L.C. = 5 µm = 0.005 mm

Rearranging the formula to find the number of divisions (n):

n = Pitch / L.C.

Substituting the values:

n = 1 mm / 0.005 mm

n = 200

Final Answer:

The minimum number of divisions required on the circular scale of the screw gauge to measure 5 µm is 200.

Conclusion:

The least count of screw gauge determines its precision. By ensuring that the circular scale has at least 200 divisions, the screw gauge can measure dimensions as small as 5 µm accurately.