17. NCERT line-by-line

1. TITLE

NCERT says 'represented by the sides of a closed n-sided polygon' — Here's how NEET tests it

2. THE NCERT STATEMENT

NCERT EXACT LINE:
"A particle is in equilibrium under the action of forces $F_{1}$, $F_{2},...F_{n}$ if they can be represented by the sides of a closed n-sided polygon with arrows directed in the same sense."
— NCERT Class 11, Chapter 4, Page 58

3. WHY THIS LINE MATTERS

  • How many times has NEET tested this? Vector addition, equilibrium conditions, and Lami's theorem are tested almost every year, directly or indirectly.
  • What makes this statement tricky? Students often ignore the geometric aspect of equilibrium. They know mathematically that $\Sigma F = 0$, but fail to visualize that graphically, the vectors must loop perfectly back to the origin.
  • What do students typically misremember? Students frequently misremember the condition for the arrows. They might think any closed polygon guarantees equilibrium, ignoring the critical requirement that the arrows must be directed in the "same sense" (head-to-tail). Students also misremember that equilibrium means the body must be at rest, forgetting that uniform motion (constant velocity) is also a valid state of equilibrium.

4. MCQ (Directly from this NCERT line)

According to NCERT, a particle is in equilibrium under the action of multiple concurrent forces $F_{1}$, $F_{2},...F_{n}$ if these forces can be represented by:
A) The sides of a closed n-sided polygon with arrows directed in the same sense.
B) The sides of a closed n-sided polygon with arrows directed in opposite senses.
C) The diagonals of a closed n-sided polygon.
D) An open n-sided polygon with arrows in the same sense.

5. ANSWER + LINE BREAKDOWN

Correct Answer: A

Break down the NCERT line:
- "equilibrium under the action of forces" means the net external force acting on the particle is zero, meaning it is either strictly at rest or moving with uniform motion.
- "sides of a closed n-sided polygon" means that when you geometrically add all the force vectors, the final vector's head touches the first vector's tail, resulting in a resultant vector of zero.
- The key word is "same sense" because to apply the polygon law of vector addition correctly to get a zero resultant, every force vector must be placed head-to-tail continuously.

6. HOW NEET TWISTS THIS

Show 3 ways NEET can ask the same fact:
- As direct question: "If three concurrent forces acting on a particle are represented in magnitude and direction by the sides of a triangle taken in the same order, what is the net force acting on the particle?" (Answer: Zero, the particle is in equilibrium).
- As assertion-reason: Assertion: A particle moving with constant velocity under the influence of three forces is in equilibrium. Reason: The three forces can be represented by the sides of a closed triangle with vector arrows taken in the same sense.
- As an except question: "All of the following indicate that a particle is in translational equilibrium EXCEPT: A) The net external force is zero. B) It is moving with constant velocity. C) Its forces form a closed polygon taken in the same sense. D) It has constant but non-zero acceleration." (Answer: D).

7. MEMORY LOCK

MEMORIZE:
Closed Polygon + Same Sense Arrows = Zero Net Force (Equilibrium).
Mnemonic: Closed Shape, Same Sense = Stationary (or Steady speed).

8. RELATED NCERT LINES

Also remember these from the same page:
- "Equilibrium of a particle in mechanics refers to the situation when the net external force on the particle is zero."
- "According to the first law, this means that, the particle is either at rest or in uniform motion."
- "If two forces $F_{1}$ and $F_{2}$, act on a particle, equilibrium requires $F_{1} = -F_{2}$."

9. NCERT REFERENCE

NCERT Class 11, Chapter 4, Page 58, Paragraph 3.

10. CTA

All important NCERT lines from this chapter → 3-Laws of Motion Guide