Question

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 θ . 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 sinθ 
(D) When the bar makes an angle q with the vertical, the displacement of its midpoint from the initial position is proportional to (1 – cosθ)

Answer 1

(A, C, D)
As F_x = 0, a_x = 0. Therefore the force acting in vertical direction will move the mid point of the bar fall vertically downwards. (A) is correct option.

When the bar makes an angle q with the vertical, the
displacement of its mid point from the initial position is L/2 - L/2cosθ

(D) is a correct option.
Instantaneous torque about the point of contact P is