11th Class Physics Chapter 2 Notes | Get Now
11th Class Physics Chapter 2 Notes are one of the most important study resources for matric and intermediate students following the Punjab Board syllabus. Chapter 2 is titled Vectors and Equilibrium, and it lays the foundation for understanding forces, motion, and physical quantities throughout the rest of the physics course. Whether you are preparing for board exams or class tests, mastering this chapter is essential.
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This chapter covers topics like unit vectors, position vectors, rectangular components, dot product, cross product, torque, and conditions of equilibrium. These concepts appear frequently in both short questions and numerical problems in annual exams.
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What Is Covered in Chapter 2 – Vectors and Equilibrium?
The chapter is divided into two major parts: conceptual short questions and solved numerical problems. Both sections are equally important for scoring high marks.
Key Topics in 11th Class Physics Chapter 2
- Unit Vector – A vector with magnitude equal to one, used to show direction
- Position Vector – Describes the location of a point with respect to the origin
- Components of a Vector – The effective parts of a vector along x and y axes
- Vector Addition – Head-to-tail rule and resultant vectors
- Rectangular Components – Horizontal (Ax) and vertical (Ay) components
- Dot Product (Scalar Product) – A · B = AB cos θ
- Cross Product (Vector Product) – A × B = AB sin θ n̂
- Torque – Rotational effect of force, τ = r × F
- Conditions of Equilibrium – First condition (ΣF = 0) and second condition (Στ = 0)
Important Short Questions From Chapter 2
The short questions section of 11th Class Physics Chapter 2 Notes includes 21 questions (2.1 to 2.21). These are the most commonly asked questions in Punjab Board exams. Below is a summary of the most important ones:
Q 2.1 – Define Unit Vector, Position Vector, and Components of a Vector
- Unit Vector: A vector whose magnitude is one. Formula: Â = A→ / |A|
- Position Vector: A vector that describes the location of a particle with respect to the origin. In 3D: r→ = aî + bĵ + ck̂
- Component of a Vector: The part of a vector effective in a particular direction. One along the x-axis (horizontal) and one along the y-axis (vertical).
Q 2.4 – Can Magnitude Be Zero If a Component Is Not Zero?
No. If even one rectangular component of a vector is not zero, the magnitude of the vector cannot be zero. This is because magnitude uses the formula A = √(Ax² + Ay²), which will always give a positive result.
Q 2.6 – Can Magnitude of a Vector Be Negative?
No. The magnitude of a vector is always positive. For example, −3A→ means the direction is reversed, but the magnitude (3) stays positive.
Q 2.8 – When Are Both Components Equal in Magnitude?
When vector A makes a 45° angle with the x-axis, then Ax = Ay. This is because tan 45° = 1, which means Ay/Ax = 1.
Q 2.11 – Can Two Vectors of Unequal Magnitudes Give Zero Sum?
No. The sum of two vectors of unequal magnitudes can never be zero. Two vectors can only cancel if they have equal magnitudes and opposite directions.
Q 2.18 – Three Conditions for A₁ × A₂ = 0
Using A₁ × A₂ = A₁A₂ sin θ n̂, the cross product is zero if:
- Either A₁ or A₂ is a null vector
- A₁ and A₂ are parallel (θ = 0°)
- A₁ and A₂ are anti-parallel (θ = 180°)
Q 2.21 – Can a Body Rotate About Its Centre of Gravity Under Its Own Weight?
No. Since the line of action of weight passes through the centre of gravity (pivot), the moment arm r = 0. So τ = rF = 0 × F = 0.
Solved Problems in 11th Class Physics Chapter 2 Notes
The problems section includes 18 solved numerical problems (Problem 2.1 to 2.18). These cover all major formulas of the chapter. Here are the most important ones students must practice:
Problem 2.1 – Distance Between Two Points
A vector A→ has its tail at P(−2, −3) and tip at Q(3, 9). Using position vectors:
- r₂ − r₁ = 5î + 12ĵ
- Distance = √(5² + 12²) = √169 = 13 units
Problem 2.3 – Finding the Unit Vector
For A→ = 4î + 3ĵ:
 = A→ / |A| = (4î + 3ĵ) / √(16+9) = (4î + 3ĵ) / 5
Problem 2.7 – Angle Between Two Vectors
For A→ = 5î + ĵ and B→ = 2î + 4ĵ:
- A · B = 10 + 4 = 14
- A = √26 ≈ 5.1, B = √20 ≈ 4.5
- cos θ = 14 / (5.1 × 4.5) = 0.61
- θ = 52°
Problem 2.14 – Angle From Dot and Cross Products
Given: dot product = 6√3, cross product = 6
- tan θ = (cross/dot) = 6 / 6√3 = 1/√3
- θ = 30°
Problem 2.15 – Tension in a Clothes Line
Load = 10 N, angle with horizontal = 15°
- T = Load / (2 sin θ) = 10 / (2 × 0.2588) = 19.3 N
Problem 2.17 – Minimum Force to Lift a Spherical Ball Over a Step
Weight W = 50 N, radius = 20 cm, step height = 5 cm
Using the 2nd condition of equilibrium:
- F = 26 N
Problem 2.18 – Tension in String and Force by Wall
Weight = 10 N, angle with wall = 30°
- T = W / cos θ = 10 / 0.866 = 11.55 N
- F = T sin θ = 11.55 × sin 30° = 5.8 N
How to Study 11th Class Physics Chapter 2 Effectively
Using 11th Class Physics Chapter 2 Notes the right way can save time and boost marks. Here are some study tips:
- Memorize definitions first – Unit vector, position vector, and components are always asked
- Practice all 18 problems – Numerical problems carry heavy weightage in board exams
- Understand the equilibrium conditions – Both first and second conditions must be clear
- Draw vector diagrams – Visual understanding helps solve problems faster
- Revise cross and dot product rules – These appear in both theory and numericals
- Use past papers – Match questions from these notes with previous board papers
For more chapter-wise notes, check out the [internal link] for 11th Class Physics complete notes on TaleemWorld.com.
Why These Notes Are Best for Punjab Board Students
These 11th Class Physics Chapter 2 Notes are specifically written for students following the Punjab Board (BISE) syllabus. The notes follow the exact pattern of annual board exams and include:
- All short questions with complete answers
- Step-by-step solved problems with data, formula, and result sections
- Diagrams and vector illustrations
- Equilibrium-based problems with torque calculations
Students preparing for FSc Part 1 or 1st Year Physics will find these notes especially helpful for last-minute revision before board exams.
FAQs – 11th Class Physics Chapter 2 Notes
Q1: What is Chapter 2 of 11th Class Physics about?
Chapter 2 of 11th Class Physics is titled Vectors and Equilibrium. It covers unit vectors, position vectors, vector components, dot and cross products, torque, and both conditions of equilibrium. It is one of the most important chapters for Punjab Board exams.
Q2: Where can I get 11th Class Physics Chapter 2 Notes for Punjab Board?
You can get complete 11th Class Physics Chapter 2 Notes on TaleemWorld.com. The notes include all short questions with answers and 18 fully solved numerical problems, covering all topics in the Punjab Board syllabus.
Q3: How many short questions are in Chapter 2 of Physics 11th Class?
There are 21 short questions (numbered 2.1 to 2.21) in Chapter 2 of 11th Class Physics. These questions cover all major concepts including vectors, equilibrium, torque, and properties of vector operations.
Q4: What is the formula for the unit vector in Physics Chapter 2?
The formula for a unit vector is  = A→ / |A|. It divides the original vector by its magnitude, giving a vector with magnitude equal to 1 that shows only the direction of the original vector.
Q5: How many problems are solved in Chapter 2 Physics 11th Class Notes?
There are 18 solved problems (Problem 2.1 to Problem 2.18) in Chapter 2. They include problems on distance between points, unit vectors, dot product, cross product, torque, equilibrium, tension in strings, and bridge support forces.
Q6: What are the two conditions of equilibrium in 11th Class Physics?
The first condition of equilibrium states that the sum of all forces must be zero (ΣF = 0). The second condition states that the sum of all torques must be zero (Στ = 0). Both conditions are explained with examples in Chapter 2 notes.