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 Introduction of Units and Measurements
Physical World and Measurement
Motion in a Straight Line
 Position, Path Length and Displacement
 Average Velocity and Average Speed
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 Kinematic Equations for Uniformly Accelerated Motion
 Acceleration (Average and Instantaneous)
 Relative Velocity
 Elementary Concept of Differentiation and Integration for Describing Motion
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 Position  Time Graph
 Relations for Uniformly Accelerated Motion (Graphical Treatment)
 Introduction of Motion in One Dimension
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Kinematics
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 General Vectors and Their Notations
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 Relative Velocity in Two Dimensions
 Cases of Uniform Velocity
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 Introduction of Motion in One Dimension
Laws of Motion
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 Aristotle’s Fallacy
 The Law of Inertia
 Newton's First Law of Motion
 Newton’s Second Law of Motion
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 Common Forces in Mechanics
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 Static and Kinetic Friction
 Laws of Friction
 Inertia
 Intuitive Concept of Force
 Dynamics of Uniform Circular Motion  Centripetal Force
 Examples of Circular Motion (Vehicle on a Level Circular Road, Vehicle on a Banked Road)
 Lubrication  (Laws of Motion)
 Law of Conservation of Linear Momentum and Its Applications
 Rolling Friction
 Introduction of Motion in One Dimension
Work, Energy and Power
Motion of System of Particles and Rigid Body
Work, Energy and Power
 Introduction of Work, Energy and Power
 Notions of Work and Kinetic Energy: the Workenergy Theorem
 Kinetic Energy
 Work Done by a Constant Force and a Variable Force
 Concept of Work
 The Concept of Potential Energy
 Conservation of Mechanical Energy
 Potential Energy of a Spring
 Various Forms of Energy : the Law of Conservation of Energy
 Power
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 Non  Conservative Forces  Motion in a Vertical Circle
Gravitation
System of Particles and Rotational Motion
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 Centre of Mass
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 Linear Momentum of a System of Particles
 Vector Product of Two Vectors
 Angular Velocity and Its Relation with Linear Velocity
 Torque and Angular Momentum
 Equilibrium of Rigid Body
 Moment of Inertia
 Theorems of Perpendicular and Parallel Axes
 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
 Momentum Conservation and Centre of Mass Motion
 Centre of Mass of a Rigid Body
 Centre of Mass of a Uniform Rod
 Rigid Body Rotation
 Equations of Rotational Motion
 Comparison of Linear and Rotational Motions
 Values of Moments of Inertia for Simple Geometrical Objects (No Derivation)
Gravitation
 Kepler’s Laws
 Newton’s Universal Law of Gravitation
 The Gravitational Constant
 Acceleration Due to Gravity of the Earth
 Acceleration Due to Gravity Below and Above the Earth's Surface
 Acceleration Due to Gravity and Its Variation with Altitude and Depth
 Gravitational Potential Energy
 Escape Speed
 Earth Satellites
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Properties of Bulk Matter
Thermodynamics
Mechanical Properties of Solids
 Elastic Behaviour of Solid
 Stress and Strain
 Hooke’s Law
 Stressstrain Curve
 Young’s Modulus
 Determination of Young’s Modulus of the Material of a Wire
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 Application of Elastic Behaviour of Materials
 Elastic Energy
 Poisson’s Ratio
Mechanical Properties of Fluids
 Thrust and Pressure
 Pascal’s Law
 Variation of Pressure with Depth
 Atmospheric Pressure and Gauge Pressure
 Hydraulic Machines
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 Applications of Bernoulli’s Equation
 Viscous Force or Viscosity
 Reynold's Number
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 Terminal Velocity
 Critical Velocity
 Excess of Pressure Across a Curved Surface
 Introduction of Mechanical Properties of Fluids
 Archimedes' Principle
 Stoke's Law
 Equation of Continuity
 Torricelli's Law
Behaviour of Perfect Gases and Kinetic Theory of Gases
Oscillations and Waves
Thermal Properties of Matter
 Heat and Temperature
 Measurement of Temperature
 Idealgas Equation and Absolute Temperature
 Thermal Expansion
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 Calorimetry
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 Newton’s Law of Cooling
 Qualitative Ideas of Black Body Radiation
 Wien's Displacement Law
 Stefan's Law
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 Liquids and Gases
 Thermal Expansion of Solids
 Green House Effect
Thermodynamics
 Thermal Equilibrium
 Zeroth Law of Thermodynamics
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 First Law of Thermodynamics
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 Thermodynamic Process
 Heat Engine
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 Second Law of Thermodynamics
 Reversible and Irreversible Processes
 Carnot Engine
Kinetic Theory
 Molecular Nature of Matter
 Gases and Its Characteristics
 Equation of State of a Perfect Gas
 Work Done in Compressing a Gas
 Introduction of Kinetic Theory of an Ideal Gas
 Interpretation of Temperature in Kinetic Theory
 Law of Equipartition of Energy
 Specific Heat Capacities  Gases
 Mean Free Path
 Kinetic Theory of Gases  Concept of Pressure
 Assumptions of Kinetic Theory of Gases
 RMS Speed of Gas Molecules
 Degrees of Freedom
 Avogadro's Number
Oscillations
 Periodic and Oscillatory Motion
 Simple Harmonic Motion (S.H.M.)
 Simple Harmonic Motion and Uniform Circular Motion
 Velocity and Acceleration in Simple Harmonic Motion
 Force Law for Simple Harmonic Motion
 Energy in Simple Harmonic Motion
 Some Systems Executing Simple Harmonic Motion
 Damped Simple Harmonic Motion
 Forced Oscillations and Resonance
 Displacement as a Function of Time
 Periodic Functions
 Oscillations  Frequency
 Simple Pendulum
Waves
 Reflection of Transverse and Longitudinal Waves
 Displacement Relation for a Progressive Wave
 The Speed of a Travelling Wave
 Principle of Superposition of Waves
 Introduction of Reflection of Waves
 Standing Waves and Normal Modes
 Beats
 Doppler Effect
 Wave Motion
 Speed of Wave Motion
 Gravitational Potential Energy and Gravitational Potential
Notes
Gravitational Potential Energy

Potential energy is due to the virtue of position of the object.

Gravitational Potential Energy is due to the potential energy of a body arising out of the force of gravity.

Consider a particle which is at a point P above the surface of earth and when it falls on the surface of earth at position Q, the particle is changing its position because of force of gravity.

The change in potential energy from position P to Q is same as the work done by the gravity.

It depends on the height above the ground and mass of the body.
Expression for gravitational potential energy:
Case 1: 'g' is Constant.
Consider an object of mass 'm' at point A on the surface of the earth.
work done will be given as;
`"W"_("BA")="FX"` Displacement where F=gravitational force exerted towards the earth.
=mg(h_{2}h_{1}) (body is brought from position A to B)
=mgh_{2}  mgh_{1}
W_{AB = }V_{A  }V_{B }
Where,
V_{A} = potential energy at point A
V_{B} = Potential energy at point B
From above equation we can say that the work done in moving the particle is just the difference of potential energy between its final and initial positions.
Case 2: 'g' is not constant.
Calculate work done in lifting a particle from r = r_{1} to r = r_{2}(r_{2} > r_{1}) along a vertical path .
we will get, W=V(r_{2})  V(r_{1})
Conclusion:
In general the gravitational potential energy at a distance 'r' is given by `"V"(r)=("GM"_em)/"r" + "V"_o`
where,
V(r)= potential energy at a distance 'r'.
V_{o} = At this point gravitational potential energy is zero.
Gravitational potential energy is `prop` to the mass of the particle.
Problem:
Choose the correct alternative:
 Acceleration due to gravity increases/decreases with increasing altitude.
 Acceleration due to gravity increases/decreases with increasing depth. (assume the earth to be a sphere of uniform density).
 Acceleration due to gravity is independent of mass of the earth/mass of the body.
 The formula – `GMm(1/r_2– 1/r_1)` is more/less accurate than the formula `"mg"(r_2– r_1)` for the difference of potential energy between two points r_{2}and r_{1} distance away from the centre of the earth.
Answer:
(a)Decreases
(b)Decreases
(c)Mass of the body
(d)More
Explanation:
Acceleration due to gravity at depth h is given by the relation:
`"gh" = (1 "2h"/R_E)g`
Where,
R_{E} = Radius of the Earth, g = acceleration due to gravity on the surface of the earth.
It is clear from the given relation that acceleration due to gravity decreases with an increase in height.
Acceleration due to gravity at depth d is given by the relation:
`"gd"=(1"d"/"R"_E)g`
It is clear from the given relation that acceleration due to gravity decreases with an increase in depth.
Acceleration due to gravity of body of mass m is given by the relation: `"g"="GM"/"r"^2`
Where,
G = Universal gravitational constant
M = Mass of the Earth
R = Radius of the Earth
Hence, it can be inferred that acceleration due to gravity is independent of the mass of the body.
Gravitational potential energy of two points r_{2} and r_{1} distance away from the centre of the Earth is respectively given by:
`"V"(r_1) =  "GmM"/r_1`
`"V"(r_2) = "GmM"/r_2`
Therefore,
Difference in potential energy, V = V(r_{2}) – V(r1) =GmM (1/r_{2} – 1/r_{1})
Hence, this formula is more accurate than the formula mg (r_{2}– r_{1}).