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 vortical 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 sin θ

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

Answer 1

(A) The midpoint of the bar will fall vertically downward

(C) Instantaneous torque about the point in contact with the floor is proportional to sin θ

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

There is no horizontal force on rod during its motion

⇒ C.M. will fall vertically downwards

Net torque about point B(on the ground) = mgL sin θ

Displacement mid point \(=\frac{L}{2}-\frac{L}{2}\) cosθ