2. As shown in Figure $1, A B$ is the diameter of the semicircle $\odot O$, and $C$ is a point on the semicircle, with $\angle C O A = 60^{\circ}$. Let the areas of the sector $A O C$, $\triangle C O B$, and the segment $B m C$ be $S_{1}, S_{2}, S_{3}$, respectively. Then the size relationship among them is ( ).
(A) $S_{1}<S_{2}<S_{3}$
(B) $S_{2}<S_{1}<S_{3}$
(C) $S_{1}<S_{3}<S_{2}$
(D) $S_{3}<S_{2}<S_{1}$
2. B.

Let the radius of the semicircle be 1, then
$$
S_{1}=\frac{\pi}{6}, S_{2}=\frac{\sqrt{3}}{4}, S_{3}=\frac{\pi}{3}-\frac{\sqrt{3}}{4} \text {. }
$$

Therefore, $S_{2}<S_{1}<S_{3}$.