A rigid uniform bar AB of length L is slipping from its vertical position on a frictionless floor (as shown in the figure). At some instant of time, the angle made by the bar with the vertical is $$\theta$$ Which of the following statements about its motion is/are correct?

A

The midpoint of the bar will fall vertically downward

B

The trajectory of the point A is a parabola

C

Instantaneous torque about the point in contact with the floor is proportional to $$sin\ \theta$$

D

When the bar makes an angle $$\theta$$ with the vertical, the displacement of its midpoint from the initial position is proportional to $$(1-Cos\ \theta)$$