A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is

The correct option is πD/T.

Step-by-Step Explanation:

1. Definition of Circular Pitch:
The circular pitch (denoted by $p$) of a gear is the distance measured along the pitch circle circumference from a point on one tooth to the corresponding point on the adjacent tooth.

2. Derivation of the Formula:
The total circumference of the pitch circle of a gear with pitch circle diameter $D$ is given by:
$\text{Circumference}=\pi D$

Since the gear has $T$ number of teeth, the circular pitch is simply the total circumference of the pitch circle divided by the total number of teeth:

$p=\frac{\pi D}{T}$

Therefore, the circular pitch of the gear is $\frac{\pi D}{T}$, which matches the correct option.