Equilibrium of a Particle Class 11 Physics Notes, MCQs, Questions and Answers

 Equilibrium of a Particle Class 11 CBSE Notes with Question Bank

Equilibrium of a Particle showing balanced forces, vector addition, and equilibrium conditions in Class 11 Physics.

-  Dr.Sanjaykumar Pawar 

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System of Particles and Rotational Motion

Gravitation Class 11 Notes

Mechanical Properties of Solids

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Class 11 Physics MCQ Collection

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Physics Formula Sheet Class 11

Equilibrium of a Particle (NEET Level Notes)

1. Meaning of Equilibrium

• Equilibrium means a body is balanced under the action of forces.
• A particle is said to be in equilibrium when the net external force acting on it is zero.
• The resultant force acting on the particle becomes zero.

ΣF = 0

• Here, ΣF represents the vector sum of all forces acting on the particle.

2. Condition of Equilibrium

• If the resultant of all forces is zero, the particle is in equilibrium.
• According to Newton's First Law of Motion:

• The particle may remain at rest.
• The particle may move with constant velocity.

Important: Zero net force does not always mean the object is at rest. It can also move with uniform velocity.

3. Equilibrium Under Two Forces

Suppose two forces F₁ and F₂ act on a particle.

F₁ = −F₂

Conditions

• The two forces must have equal magnitude.
• The two forces must act in opposite directions.
• The two forces must act along the same straight line.

Example

• A book resting on a table.
• Weight acts downward.
• Normal reaction acts upward.
• Both forces are equal and opposite.
• Hence the book remains in equilibrium.

4. Equilibrium Under Three Concurrent Forces

Concurrent forces are forces whose lines of action pass through the same point.

Suppose three forces F₁, F₂ and F₃ act on a particle.

F₁ + F₂ + F₃ = 0

Meaning

• The vector sum of all three forces is zero.
• The resultant of any two forces is equal and opposite to the third force.

5. Triangle Law of Equilibrium

• Three forces in equilibrium can be represented by the three sides of a triangle.
• The vectors should be drawn head-to-tail in the same order.
• The triangle formed should be closed.
• A closed triangle indicates zero resultant force.

Three concurrent forces are in equilibrium if they can be represented completely by the sides of a triangle taken in order.

6. Equilibrium Under Many Forces

Suppose many forces F₁, F₂, F₃, ... Fn act on a particle.

F₁ + F₂ + F₃ + ... + Fn = 0

Polygon Law of Equilibrium

• If all forces can be represented by the sides of a closed polygon, the particle is in equilibrium.
• The arrows of all vectors should be taken in the same order.
• The resultant force becomes zero.

Remember

• Closed Triangle → Three Forces
• Closed Polygon → Many Forces

7. Equilibrium in Terms of Components

Every force can be resolved into components along x, y and z directions.

• F₁x = x-component of force F₁
• F₁y = y-component of force F₁
• F₁z = z-component of force F₁

For equilibrium, the sum of force components along each axis must be zero.

Along X-axis

F₁x + F₂x + F₃x = 0

Along Y-axis

F₁y + F₂y + F₃y = 0

Along Z-axis

F₁z + F₂z + F₃z = 0

8. Physical Meaning of Component Equations

• Forces along +x and −x directions balance each other.
• Forces along +y and −y directions balance each other.
• Forces along +z and −z directions balance each other.
• Hence no acceleration is produced in any direction.

9. NEET Quick Revision Table

Situation	Condition for Equilibrium
Two Forces	Equal and Opposite
Three Forces	Closed Triangle
Many Forces	Closed Polygon
X-direction	ΣFx = 0
Y-direction	ΣFy = 0
Z-direction	ΣFz = 0
Net Force	ΣF = 0

NEET Summary: A particle is said to be in equilibrium when the vector sum of all external forces acting on it is zero (ΣF = 0). In equilibrium, the particle remains either at rest or moves with constant velocity.

Equilibrium of a Particle - Mind Map (Plain Text Tree)

EQUILIBRIUM OF A PARTICLE │ ├── Definition │ │ │ ├── Net external force = 0 │ ├── Resultant force = 0 │ └── ΣF = 0 │ ├── According to Newton's First Law │ │ │ ├── Particle remains at rest │ └── Particle moves with uniform velocity │ ├── Equilibrium Under Two Forces │ │ │ ├── F₁ = −F₂ │ ├── Equal magnitude │ ├── Opposite direction │ └── Same line of action │ ├── Equilibrium Under Three Forces │ │ │ ├── F₁ + F₂ + F₃ = 0 │ ├── Concurrent forces │ ├── Resultant of two forces │ │ = Opposite of third force │ └── Vector sum = 0 │ ├── Triangle Law of Equilibrium │ │ │ ├── Three forces form a triangle │ ├── Head-to-tail arrangement │ ├── Closed triangle │ └── Resultant force = 0 │ ├── Equilibrium Under Many Forces │ │ │ ├── F₁ + F₂ + F₃ + ... + Fn = 0 │ ├── Polygon Law │ ├── Closed polygon formed │ └── Resultant force = 0 │ ├── Resolution of Forces │ │ │ ├── Components along X-axis │ ├── Components along Y-axis │ └── Components along Z-axis │ ├── Conditions in Component Form │ │ │ ├── ΣFx = 0 │ ├── ΣFy = 0 │ └── ΣFz = 0 │ ├── Physical Meaning │ │ │ ├── Forces balance in X-direction │ ├── Forces balance in Y-direction │ ├── Forces balance in Z-direction │ └── No acceleration produced │ └── NEET Quick Facts │ ├── Two forces → Equal & Opposite ├── Three forces → Closed Triangle ├── Many forces → Closed Polygon ├── ΣFx = 0 ├── ΣFy = 0 ├── ΣFz = 0 └── ΣF = 0 ⇒ Equilibrium

CBSE Class 11 Physics

Equilibrium of a Particle - Question Bank

A. Multiple Choice Questions (MCQs)

1. A particle is said to be in equilibrium when:

(a) Velocity is zero

(b) Acceleration is zero

(c) Net force is zero

(d) Displacement is zero

Answer: (c) Net force is zero

2. If two forces keep a particle in equilibrium, they must be:

(a) Equal

(b) Opposite

(c) Equal and opposite

(d) Perpendicular

Answer: (c) Equal and opposite

3. The SI unit of force is:

(a) Joule

(b) Newton

(c) Watt

(d) Pascal

Answer: (b) Newton

4. For equilibrium in three dimensions:

(a) ΣFx = 0

(b) ΣFy = 0

(c) ΣFz = 0

(d) ΣFx = ΣFy = ΣFz = 0

Answer: (d)

5. Three concurrent forces in equilibrium form:

(a) Circle

(b) Triangle

(c) Rectangle

(d) Ellipse

Answer: (b) Triangle

B. Very Short Answer Questions (1 Mark)

1. What is equilibrium?

Answer: Equilibrium is the state when the net external force acting on a particle is zero.

2. Write the condition for equilibrium.

Answer: ΣF = 0

3. What is the resultant force on a particle in equilibrium?

Answer: Zero.

4. What are concurrent forces?

Answer: Forces whose lines of action meet at a single point.

5. Can a moving particle be in equilibrium?

Answer: Yes, if it moves with constant velocity.

C. Short Answer Questions (2–3 Marks)

1. State the conditions for equilibrium under two forces.

Answer:
1. Forces must be equal in magnitude.
2. Forces must act in opposite directions.
3. Forces must act along the same line.

2. Explain triangle law of equilibrium.

Answer: If three forces acting on a particle can be represented by the sides of a triangle taken in order, the particle is in equilibrium.

3. What are the component equations of equilibrium?

Answer:
ΣFx = 0
ΣFy = 0
ΣFz = 0

D. Long Answer Questions (5 Marks)

1. Explain equilibrium of a particle.

Answer: A particle is said to be in equilibrium when the vector sum of all external forces acting on it is zero.

Condition:
ΣF = 0

According to Newton's First Law:
• The particle remains at rest, or
• Moves with uniform velocity.

For three-dimensional equilibrium:
ΣFx = 0
ΣFy = 0
ΣFz = 0

All three conditions must be satisfied simultaneously.

2. Explain equilibrium under three concurrent forces.

Answer:
For three concurrent forces:
F₁ + F₂ + F₃ = 0

The resultant of any two forces is equal and opposite to the third force.

These forces can be represented by the sides of a closed triangle.

This is called Triangle Law of Equilibrium.

E. Assertion and Reason Questions

Assertion (A): A particle can move with constant velocity in equilibrium.
Reason (R): Net external force acting on it is zero.

Answer: Both Assertion and Reason are true and Reason correctly explains Assertion.

Assertion (A): Three concurrent forces in equilibrium form a triangle.
Reason (R): Their vector sum is zero.

Answer: Both Assertion and Reason are true and Reason correctly explains Assertion.

F. Fill in the Blanks

1. A particle is in equilibrium when the ______ force acting on it is zero.

Answer: resultant

2. According to Newton's ______ law, equilibrium implies rest or uniform motion.

Answer: first

3. Three forces in equilibrium form a closed ______.

Answer: triangle

4. Many forces in equilibrium form a closed ______.

Answer: polygon

G. Statement-Based Questions

Statement I: A particle in equilibrium may be moving.
Statement II: A particle in equilibrium has zero acceleration.

Answer: Both statements are true.

Statement I: Three forces in equilibrium form a closed triangle.
Statement II: Their vector sum is zero.

Answer: Both statements are true.

H. Match the Columns

Column A	Column B
1. Equilibrium	A. Closed Triangle
2. Three Forces	B. Net Force Zero
3. Polygon Law	C. Closed Polygon
4. Concurrent Forces	D. Meet at One Point

Answers
1 → B
2 → A
3 → C
4 → D

I. Case Study Questions

A signboard is hanging by two ropes. The forces acting on it are:

• Weight acting downward
• Tension T₁ in first rope
• Tension T₂ in second rope

The signboard remains at rest.

1. How many forces act on the signboard?

Answer: Three forces.

2. Is the signboard in equilibrium?

Answer: Yes.

3. What is the resultant force acting on it?

Answer: Zero.

4. Which law explains this equilibrium?

Answer: Newton's First Law of Motion.

5. Which geometric figure represents these forces?

Answer: Triangle.

J. HOTS Questions

1. Can a car moving with constant velocity be in equilibrium? Explain.

Answer: Yes. Constant velocity means zero acceleration. Therefore the net force acting on the car is zero and the car is in equilibrium.

2. Why is balancing of forces necessary for equilibrium?

Answer: Unbalanced forces produce acceleration. For equilibrium, acceleration must be zero. Therefore all forces must balance each other.

K. Important Formulae

ΣF = 0

ΣFx = 0

ΣFy = 0

ΣFz = 0

F₁ + F₂ + F₃ = 0

F₁ = −F₂