In a V-thread, a wire is fitted such that it makes contact with the flank of the thread on the pitch line as shown in the figure. If the pitch p of the thread is 3 mm and the included angle is 60°, the diameter (in mm, up to one decimal place) of the wire is ________.

This question was previously asked in

GATE PI 2018 Official Paper

**Concept:**

**Best size wire Method:** In this, the **wire is of such diameter that** **it makes contact with the flanks of the thread** on the effective diameter or pitch line. The effective diameter can be measured with any diameter wire which makes contact on the true flank of the thread.

Wire diameter in this case is given by

\(d = \frac {p}{2} \left((\sec \left(\frac α 2 \right)\right )\)

Where **p** = pitch; **α** = Thread angle;

**Calculation:**

**Given:**

p = 3 mm; α = 60°;

\(d = \frac {p}{2} \left((\sec \left(\frac α 2 \right)\right )\) = \(\frac {3}{2} \left((\sec \left(\frac {60} {2} \right)\right )\)

**d = 1.73 mm.**