Physics Question from JEE Main 2023 · 30 January, Shift 1

In a screw gauge, there are $100$ divisions on the circular scale and the main scale moves by $0.5 \, \text{mm}$ 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 the **$46$**th division the circular scale coincide with the reference line. The diameter of the wire is _____ $\times 10^{-2}$ mm.