A solid cube of wood of side \( 2 a \) and mass \( M \) is resting on a horizontal surface as shown in the figure. The cube is free to rotate about a fixed axis \( A B \). A bullet of mass \( m(< < M) \) and speed \( v \) is shot horizontally at the face opposite to \( A B C D \) at a height of \( \frac{4 a}{3} \) from the surface to impart the cube and angular speed \( \omega \). It strikes the face and embeds in the cube. Then \( \omega \) is close to (note: the moment of inertia of the cube about an axis perpendicular to the face and passing through the center of mass is \( \frac{2 M a^{2}}{3} . \) )