生成这道题的解析---**Question Number:** 2.
**Question Stem:**
如图, 菱形ABCD的边长为4, ∠B=120°, E是BC的中点, F是对角线AC上的动点, 连接EF. 将线段EF绕点F按逆时针旋转30°, G为点E对应点, 连接CG, 则CG的最小值为 ( )
**Geometric Figure Description:**
* Type: Geometric diagram.
* Elements:
* A rhombus ABCD is shown.
* Vertices A, B, C, D are labeled.
* Angle B is an obtuse angle (stated as 120° in the text).
* Side length is stated as 4 in the text.
* Point E is on side BC, appearing to be the midpoint (stated as midpoint in the text).
* Diagonal AC is drawn.
* Point F is on the diagonal AC.
* Line segments EF, FG, and CG are drawn.
* Point G is positioned such that rotating EF around F counterclockwise by 30° results in FG, where G is the image of E under this rotation (stated in the text).
**Options:**
A. $\sqrt{2}$
B. $\sqrt{3}$
C. $\sqrt{2}-1$
D. $\sqrt{3}-1$