Given data

• Pitch / least count of main scale of screw gauge $= 1\,\text{mm}$
• Diameter to be measured accurately $= 5\,\mu\text{m}$

Convert the required measurement into mm $1\,\mu\text{m} = 10^{-3}\,\text{mm}$ So, $5\,\mu\text{m} = 5 \times 10^{-3}\,\text{mm} = 0.005\,\text{mm}$

Least count formula for screw gauge $\text{Least Count} = \frac{\text{Pitch}}{\text{Number of circular scale divisions}}$

Let the number of circular scale divisions be $N$. Then, $\frac{1\,\text{mm}}{N} = 0.005\,\text{mm}$

Solve for $N$ $N = \frac{1}{0.005} = 200$

Check options

• A: $500$ ❌
• B: $100$ ❌
• C: $200$ ✅
• D: $50$ ❌

Final answer The minimum number of divisions required on the circular scale is $\boxed{200}$ So, the correct option is C.