Statics — Equilibrium Condition for a Rigid Body If the resultant (net force) of a number of forces acting on a body is zero, does it automatically imply that the body is not in equilibrium?

Introduction / Context: In engineering mechanics, equilibrium for a rigid body requires that both the net force and the net moment about any point are zero. The prompt claims that a zero resultant force means the body will not be in equilibrium, which tests understanding of complete equilibrium conditions.

Given Data / Assumptions:

• A body (rigid body perspective, not just a particle).
• Multiple forces act on the body; their vector sum is zero.
• No other information about moments is given.

Concept / Approach: For a particle, equilibrium is achieved if the net force is zero. For a rigid body, two independent requirements must be met: ΣF = 0 and ΣM = 0. If only ΣF = 0 is satisfied, couple moments may still cause rotation, preventing equilibrium.

Step-by-Step Solution:

Verification / Alternative check: Consider two equal, opposite, and parallel forces forming a couple. Net force is zero but there is a net moment. The body rotates, so it is not in equilibrium despite zero resultant force.

Why Other Options Are Wrong: “Yes” contradicts rigid-body equilibrium theory; “It depends on the reference frame only” ignores the essential role of moments; “Indeterminate…” is partly true diagnostically, but the question asks whether the statement is correct—hence “No”.

Common Pitfalls: Confusing particle equilibrium (ΣF = 0) with rigid-body equilibrium (ΣF = 0 and ΣM = 0); forgetting that couples do not change ΣF but do change ΣM.

Final Answer: No, zero resultant does not by itself rule out equilibrium.