Which of the following statements about equilibrium is correct? 

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  1. Summation of all the forces acting in all the possible directions must be non-zero. 
  2. Summation of all the forces acting in all the possible directions must be zero. 
  3. Summation of all the forces acting in one direction must be zero. 
  4. Summation of all the forces acting in one direction must not be zero. 

Answer (Detailed Solution Below)

Option 2 : Summation of all the forces acting in all the possible directions must be zero. 
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Explanation:


Equilibrium refers to a condition where all the forces acting on an object are balanced. An object is said to be in equilibrium when either it remains at rest (static equilibrium) or it continues to move at a constant velocity (dynamic equilibrium).

There are two primary conditions for equilibrium:

  • The sum of all external forces acting on an object, in all possible directions, must be zero. This is known as the first or translational equilibrium condition. This results in the object's center of mass either remaining static or continuing to move at a constant velocity.
  • The sum of all external torques (moments of force) acting on the object, about any point, must be zero. This is the second or rotational equilibrium condition. This causes the object to have no angular acceleration, i.e., to either remain with a constant angular velocity or in a state of rest.

So, according to the options provided in the question, statement 2, "Summation of all the forces acting in all the possible directions must be zero," is correct. This condition is necessary for an object to be in equilibrium.

Therefore, for an object to be in equilibrium, not only must the forces in one specific direction balance each other, but the total of all forces acting on that object, from all directions, must sum to zero. Similarly, it's not sufficient for the torques about just one point to sum to zero; the torques about any and every point must do so.

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