GATE 2022 ME (ME2) – Question 56
The best size wire is fitted in a groove of a metric screw such that the wire touches the flanks of the thread on the pitch line as shown in the figure. The pitch (p) and included angle of the thread are 4 mm and 60°, respectively. The diameter of the best size wire is ______ mm (round off to 2 decimal places).
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Correct answer: 2.30 to 2.32
Explanation
**Best wire size.** The best-size wire touches the flanks at the pitch line (the points where the thread width equals the gap width). For a thread with pitch $p$ and included angle $2\alpha=\theta$:
$$d_w=\frac{p}{2\cos(\theta/2)}.$$
**Substitute** $p=4$ mm and $\theta=60^\circ$ (half angle $30^\circ$):
$$d_w=\frac{4}{2\cos30^\circ}=\frac{4}{1.7321}=2.3094\text{ mm}.$$
The diameter of the best size wire is **2.31 mm**.