An object is acted upon by a system of parallel forces causing the object to be in state equilibrium. Which of the following statement is not correct

Analysis

To solve this problem, we need to understand the conditions required for an object to be in equilibrium under a system of parallel forces.

Concept: Conditions for Equilibrium

For a body to be in equilibrium, two primary conditions must be satisfied:

1. Translational Equilibrium: The vector sum of all forces acting on the body must be zero ($\sum F = 0$). This means the sum of forces acting in one direction must be exactly balanced by the sum of forces acting in the opposite direction.
2. Rotational Equilibrium: The algebraic sum of the moments of all forces about any point must be zero ($\sum M = 0$).

Step-by-Step Evaluation

• Option A: "The resultant of the parallel forces is zero." This is correct. If the resultant were not zero, the object would accelerate in the direction of the resultant force.
• Option B: "The algebraic sum of all the moments of the forces is zero." This is correct. This is the condition for rotational equilibrium.
• Option C: "All the parallel forces must not be equal in magnitude and direction." This statement is incorrect. In a system of parallel forces, it is perfectly possible for forces to have equal magnitudes and directions (e.g., two equal upward forces balancing a downward weight). There is no rule stating they must not be equal; they simply need to satisfy the equilibrium conditions.
• Option D: "The sum of forces in one direction must be equal to the sum of forces in the opposite direction." This is correct. This is simply another way of stating that the resultant force is zero (as mentioned in Option A).

Conclusion

The question asks which statement is not correct. Since options A, B, and D are fundamental requirements for equilibrium, Option C is the statement that does not hold true as a rule.

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Exam Tip

When dealing with equilibrium questions, always remember the "Zero Rule":

• Sum of Forces = 0
• Sum of Moments = 0 If any option suggests a non-zero value for these, it is usually the "incorrect" statement you are looking for!