A uniform rod $$OA$$ of length $$L$$ is freely pivoted at one end $$O$$. Let $$C$$ be the midpoint, that is $$OC=CA=\frac L2$$. Choose the correct statement or statements.

The rod can perform small angular oscillations with time period $$T=2\pi\sqrt{\frac{L}{2g}}$$

The rod is brought to the horizontal position and then released from rest. The angular velocity of the rod at the instant when it is vertical is $$\omega=\sqrt{\frac{3g}{L}}$$

When the oscillating rod comes to the vertical position, it breaks at midpoint $$C$$ without generating any impulsive force. The largest angle from vertical reached by the upper part $$OC$$ of the rod is $$60^\circ$$

After breaking, the lower part just falls vertically rotating about its center