Test: Equilibrium of Rigid Bodies - JEE MCQ

Correct option is B.

If a dish is kept at an orientation with a marble placed on it and if the marble in figure is displaced slightly, it would rattle about for a while and come to rest in its original place.  This is the example of Stable Equilibrium.
When a body tries to regain its equilibrium position after being slightly displaced and released, it is said to be in stable equilibrium.

The stick is balanced by the 1 kg rock that is one-quarter of its length to the left and by its own weigh which is at the Centre of Mass, one-quarter of its length to the right.  Therefore, the mass of the stick must be one kilogram, 1 kg.

When two forces of equal magnitude opposite in direction and acting along parallel straight lines, then they are said to form a couple. The perpendicular distance between the two force forming a couple is called the arm of the couple.

In balanced condition torque of the both sides must be equal so Fa × Da = Fb × Db
50 × 20 = Fb × 40
Fb = 25 N

In order to rotate a body, we need to apply two equal forces at two ends but in the opposite direction.

Balance the 2 opposite moments of inertia on the 2 sides
1 × 500 = F × 5
F = 100

The line of action of F2 passes through the centre of rotation, and thus cannot produce a torque about the centre (r = 0).

In beam balance we consider the torque at centre of beam which is moment of force at its each end.

This is based on torque balance, That is F.d=const.
Therefore 3×d=5×(8-d)
by solving we get d=5.
and at point 5=E