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

The correct option is $\frac{\pi D}{T}$.

Step-by-step Explanation:
1. Definition of Circular Pitch: Circular pitch ($p_c$) is defined as the distance measured along the circumference of the pitch circle from a point on one tooth to the corresponding point on the adjacent tooth.
2. Pitch Circle Circumference: For a spur gear with a pitch circle diameter $D$, the total perimeter (circumference) of the pitch circle is given by:
$$\text{Circumference}=\pi D$$
3. Relating to Number of Teeth: If the gear has $T$ number of teeth, the circular pitch is obtained by dividing the total pitch circle circumference by the number of teeth:
$$p_c=\frac{\pi D}{T}$$
Thus, the circular pitch of the gear is $\frac{\pi D}{T}$.