Course Content
Class 11 Physics Chapter 1 Physical World
Section Name Topic Name 1 Physical World 1.1 What is physics? 1.2 Scope and excitement of physics 1.3 Physics, technology and society 1.4 Fundamental forces in nature 1.5 Nature of physical laws
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Class 11 Physics Chapter 4 Motion In A Plane
4 Motion in a plane 4.1 Introduction 4.2 Scalars and vectors 4.3 Multiplication of vectors by real numbers 4.4 Addition and subtraction of vectors – graphical method 4.5 Resolution of vectors 4.6 Vector addition – analytical method 4.7 Motion in a plane 4.8 Motion in a plane with constant acceleration 4.9 Relative velocity in two dimensions 4.10 Projectile motion 4.11 Uniform circular motion
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Class 11 Physics Chapter 5 Laws of motion
Section Name Topic Name 5 Laws of motion 5.1 Introduction 5.2 Aristotle’s fallacy 5.3 The law of inertia 5.4 Newton’s first law of motion 5.5 Newton’s second law of motion 5.6 Newton’s third law of motion 5.7 Conservation of momentum 5.8 Equilibrium of a particle 5.9 Common forces in mechanics 5.10 Circular motion 5.11 Solving problems in mechanics
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Class 11 Physics Chapter 6 Work Energy and Power
Section Name Topic Name 6 Work Energy and power 6.1 Introduction 6.2 Notions of work and kinetic energy : The work-energy theorem 6.3 Work 6.4 Kinetic energy 6.5 Work done by a variable force 6.6 The work-energy theorem for a variable force 6.7 The concept of potential energy 6.8 The conservation of mechanical energy 6.9 The potential energy of a spring 6.10 Various forms of energy : the law of conservation of energy 6.11 Power 6.12 Collisions
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Class 11 Physics Chapter 7 Rotation motion
Topics Introduction Centre of mass Motion of COM Linear Momentum of System of Particles Vector Product Angular velocity Torque & Angular Momentum Conservation of Angular Momentum Equilibrium of Rigid Body Centre of Gravity Moment of Inertia Theorem of perpendicular axis Theorem of parallel axis Moment of Inertia of Objects Kinematics of Rotational Motion about a Fixed Axis Dynamics of Rotational Motion about a Fixed Axis Angular Momentum In Case of Rotation about a Fixed Axis Rolling motion
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Class 11 Physics Chapter 9 mechanics properties of solid
Section Name Topic Name 9 Mechanical Properties Of Solids 9.1 Introduction 9.2 Elastic behaviour of solids 9.3 Stress and strain 9.4 Hooke’s law 9.5 Stress-strain curve 9.6 Elastic moduli 9.7 Applications of elastic behaviour of materials
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Class 11 Physics Chapter 11 Thermal Properties of matter
Section Name Topic Name 11 Thermal Properties of matter 11.1 Introduction 11.2 Temperature and heat 11.3 Measurement of temperature 11.4 Ideal-gas equation and absolute temperature 11.5 Thermal expansion 11.6 Specific heat capacity 11.7 Calorimetry 11.8 Change of state 11.9 Heat transfer 11.10 Newton’s law of cooling
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Class 11 Physics Chapter 14 Oscillations
Section Name Topic Name 14 Oscillations 14.1 Introduction 14.2 Periodic and oscilatory motions 14.3 Simple harmonic motion 14.4 Simple harmonic motion and uniform circular motion 14.5 Velocity and acceleration in simple harmonic motion 14.6 Force law for simple harmonic motion 14.7 Energy in simple harmonic motion 14.8 Some systems executing Simple Harmonic Motion 14.9 Damped simple harmonic motion 14.10 Forced oscillations and resonance
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About Lesson

Dimensions of a Physical Quantity

Dimensions of a physical quantity are powers (exponents) to which base quantities are raised to represent that quantity. They are represented by square brackets around the quantity.

  • Dimensions of the 7 base quantities are – Length [L], Mass [M], time [T], electric current [A], thermodynamic temperature [K], luminous intensity [cd] and amount of substance [mol].

Examples, Volume = Length x Breadth x Height = [L] x [L] x [L] = [L]3 = [L3]

Force = Mass x Acceleration = [M][L]/[T]2 = [MLT-2]

  • The other dimensions for a quantity are always 0. For example, for volume only length has 3 dimensions but the mass, time etc have 0 dimensions. Zero dimension is represented by superscript 0 like [M0].

Dimensions do not take into account the magnitude of a quantity

Dimensional Formula and Dimensional Equation

Dimensional Formula is the expression which shows how and which of the base quantities represent the dimensions of a physical quantity.

Dimensional Equation is an equation obtained by equating a physical quantity with its dimensional formula.

Physical Quantity

Dimensional Formula

Dimensional Equation

Volume

[M0 L3 T0]

[V] = [M0 L3 T0]

Speed

[M0 L T-1]

[υ] = [M0 L T-1]

Force

[M L T-2]

[F] = [M L T-2]

Mass Density

[M L-3 T0]

[ρ] = [M L-3 T0]

Dimensional Analysis

  • Only those physical quantities which have same dimensions can be added and subtracted. This is called principle of homogeneity of dimensions.
  • Dimensions can be multiplied and cancelled like normal algebraic methods.
  • In mathematical equations, quantities on both sides must always have same dimensions.
  • Arguments of special functions like trigonometric, logarithmic and ratio of similar physical quantities are dimensionless.
  • Equations are uncertain to the extent of dimensionless quantities.

Example Distance = Speed x Time. In Dimension terms, [L] = [LT-1] x [T]

Since, dimensions can be cancelled like algebra, dimension [T] gets cancelled and the equation becomes [L] = [L].

Applications of Dimensional Analysis

Checking Dimensional Consistency of equations

  • dimensionally correct equation must have same dimensions on both sides of the equation.
  • A dimensionally correct equation need not be a correct equation but a dimensionally incorrect equation is always wrong. It can test dimensional validity but not find exact relationship between the physical quantities.

Example, x = x0 + v0t + (1/2) at2Or Dimensionally, [L] = [L] + [LT-1][T] + [LT-2][T2]

x – Distance travelled in time t, x0 – starting position, v0 – initial velocity, a – uniform acceleration.

Dimensions on both sides will be [L] as [T] gets cancelled out. Hence this is dimensionally correct equation.

Deducing relation among physical quantities

  • To deduce relation among physical quantities, we should know the dependence of one quantity over others (or independent variables) and consider it as product type of dependence.
  • Dimensionless constants cannot be obtained using this method.

Example, T = k lxgymz

Or [L0M0T1] = [L1]x [L1T-2]y [M1]z= [Lx+yT-2y Mz]

Means, x+y = 0, -2y = 1 and z = 0. So, x = ½, y = -½ and z = 0

So the original equation reduces to T = k √l/g

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