Equilibrium — Triangle Law of Forces If forces acting at a point can be represented in magnitude and direction by the three sides of a triangle taken in order, then the forces are not in equilibrium.

Difficulty: Easy

Correct Answer: Disagree

Explanation:

Introduction / Context: The triangle law of forces is a fundamental condition for equilibrium of three concurrent forces. This question deliberately states the condition incorrectly to test conceptual clarity.

Given Data / Assumptions:

  • Three coplanar forces act at a point.
  • They are representable head-to-tail by the sides of a triangle taken in order.

Concept / Approach: Triangle law of forces: If three concurrent forces can be represented (in order) by the three sides of a triangle, they are in equilibrium; the resultant is zero because the vector polygon closes (returns to the start).

Step-by-Step Solution:

Represent F1, F2, F3 as vectors drawn head-to-tail. If the final head coincides with the initial tail, the vector sum F1 + F2 + F3 = 0. Zero resultant means equilibrium for a particle (no net force). Therefore, the given statement claiming 'not in equilibrium' is false.

Verification / Alternative check: Equivalent polygon law: If the vector polygon closes, the system is in equilibrium. The triangle is just the special case for three forces.

Why Other Options Are Wrong: 'Agree' supports a false statement; it contradicts standard statics results.

Common Pitfalls: Confusing the order (vectors must be taken in order, not arbitrarily); mixing up triangle law of forces with parallelogram law of vector addition (two-force case).

Final Answer: Disagree.

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