Correct Answer - Option 2 : 6

**Concept:**

Module is given by:

\(m = \frac{D}{T}\) (in mm)

where m= module, D = diameter of Gear, T = Number of teeth.

Circular pitch is given by:

\({P_c} = \frac{{π ~ \times ~D}}{T}\)

**Calculation:**

**Given**:

**P**_{c} = 6π

We have \({P_c} = \frac{{π ~ \times ~D}}{T}\) and \(m = \frac{D}{T}\)

hence,

**\(m={P_c\over \pi}={6\pi \over \pi}=6~ mm\)**

Module: It is defined as the ratio of the pitch circle diameter to the number of teeth of a gear.

\(m = \frac{D}{T}\) (in mm)

Circular pitch: It is the distance measured on the circumference of the pitch circle from a point of one tooth to the corresponding point on the tooth.

\({P_c} = \frac{{π ~ \times ~D}}{T}\)

Diametral pitch: It is the ratio of numbers of teeth to the pitch circle diameter.

\({P_d} = \frac{T}{D}\)