In considering friction of a V-thread, the virtual coefficient of friction (μ1) is given by

Answer: Option D

The virtual coefficient of friction in a V-thread is derived from the normal reaction forces and frictional forces acting on the inclined plane of the thread.

In a V-thread, the friction force is influenced by the helix angle and the thread angle ($\beta$). The relationship between the actual coefficient of friction ($\mu$) and the virtual coefficient of friction (${\mu }_1$) is determined by resolving forces along and perpendicular to the inclined thread surface.

For a V-thread, the normal force component acts at an angle, leading to the effective coefficient of friction being altered by a factor of $\cos \beta$.

Thus, the virtual coefficient of friction is given by:

$${\mu }_1=\frac{\mu }{\cos \beta }$$

This indicates that the effective friction increases as the thread angle ($\beta$) increases because the normal force component decreases, requiring a larger effective friction to compensate.