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. The pitch $p = 4$ mm and the included angle
of the thread is $60^\circ$. The diameter of the best size wire is ____________ mm
(round off to 2 decimal places).
Show Hint
For a 60° metric thread, the best wire diameter depends only on pitch:
$d = \frac{p}{2} \sec 30^\circ$.
For metric (60°) threads, the best size wire touches the flanks exactly at the pitch line.
The formula for best wire diameter in a 60° thread is:
\[
d_w = \frac{p}{2} \sec\left(\frac{\theta}{2}\right)
\]
where pitch \(p = 4\) mm and \(\theta = 60^\circ\).
Thus,
\[
d_w = \frac{4}{2} \sec 30^\circ
= 2 \times \frac{1}{\cos 30^\circ}
= 2 \times \frac{1}{0.866}
\]
\[
d_w \approx 2.309\ \text{mm}
\]
Rounded to 2 decimals:
\[
\boxed{2.31\ \text{mm}} \quad (\text{acceptable range } 2.29 \text{–} 2.33)
\]
