The least count of the main scale of a screw gauge is 1mm. The minimum number of divisions on its circular scale required to measure 5µm diameter of wire is:

The least count of a screw gauge is given by the formula:
Least Count (LC) =
(Pitch of the main scale) / (Number of divisions on the circular scale)
Given that the least count of the main scale is 1mm, and we need to measure a diameter of 5µm (5 x 10⁻³ mm), we need to find the minimum number of divisions on the circular scale.
Let's denote the number of divisions on the circular scale as 'n'.
Then, LC = 1mm / n
We need the least count to be at least as small as 5 x 10⁻³ mm to measure 5µm accurately.
Therefore, 1mm / n ≤ 5 x 10⁻³ mm
Solving for n:
n ≥ 1mm / (5 x 10⁻³ mm)
n ≥ 200
Therefore, the minimum number of divisions on the circular scale required is 200. The correct option is 200.