If D and d are external and internal diameters of a circular shaft respectively, its polar moment of inertia is

A

$$\frac{\pi(D^{4}-d^{4})}{2}$$

B

$$\frac{\pi(D^{4}-d^{4})}{4}$$

C

$$\frac{\pi(D^{4}-d^{4})}{64}$$

D

$$\frac{\pi(D^{4}-d^{4})}{32}$$