JEE Main 2023 — Experimental Physics Question with Solution

In a screw gauge, there are $100$ divisions on the circular scale and the main scale moves by $0.5 \mathrm{mm}$ on a complete rotation of the circular scale. The zero of circular scale lies $6$ divisions below the line of graduation when two studs are brought in contact with each other. When a wire is placed between the studs, $4$ linear scale divisions are clearly visible while 46^th division the circular scale coincide with the reference line. The diameter of the wire is ______ $\times {10}^{-2} \mathrm{mm}.$