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 θ 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  with the vertical, the displacement of its mid point from the initial position is l/2 -l/2 cosθ 

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

This is equation of ellipse. Therefore B is incorrect

Answer 2

Whatever be the charge and field configuration outside, any cavity in a conductor remains shielded from outside electric influence. The field inside a conductor is zero. This is known as electrostatic shielding.

Sensitive instruments are shielded from outside electrical influences by enclosing them in a hollow conductor.

During lightning it is safest to sit inside a car, rather than near a tree. The metallic body of a car becomes an electrostatic shielding from lightening.

Potential inside the cavity is not zero. Potential is constant.