#### Topics

##### Units and Measurements

- Introduction of Units and Measurements
- System of Units
- Measurement of Length
- Measurement of Mass
- Measurement of Time
- Dimensions and Dimensional Analysis
- Accuracy, Precision and Uncertainty in Measurement
- Errors in Measurements
- Significant Figures

##### Mathematical Methods

- Vector Analysis
- Vector Operations
- Resolution of Vectors
- Multiplication of Vectors
- Introduction to Calculus

##### Motion in a Plane

- Introduction to Motion in a Plane
- Rectilinear Motion
- Motion in Two Dimensions-Motion in a Plane
- Uniform Circular Motion (UCM)

##### Laws of Motion

- Introduction to Laws of Motion
- Aristotle’s Fallacy
- Newton’s Laws of Motion
- Inertial and Non-inertial Frames of Reference
- Types of Forces
- Work Energy Theorem
- Principle of Conservation of Linear Momentum
- Collisions
- Impulse of Force
- Rotational Analogue of a Force - Moment of a Force Or Torque
- Couple and Its Torque
- Mechanical Equilibrium
- Centre of Mass
- Centre of Gravity

##### Gravitation

- Introduction to Gravitation
- Kepler’s Laws
- Newton’s Universal Law of Gravitation
- Measurement of the Gravitational Constant (G)
- Acceleration Due to Gravity (Earth’s Gravitational Acceleration)
- Variation in the Acceleration Due to Gravity with Altitude, Depth, Latitude and Shape
- Gravitational Potential and Potential Energy
- Earth Satellites

##### Mechanical Properties of Solids

- Introduction to Mechanical Properties of Solids
- Elastic Behavior of Solids
- Stress and Strain
- Hooke’s Law
- Elastic Modulus
- Stress-strain Curve
- Strain Energy
- Hardness
- Friction in Solids

##### Thermal Properties of Matter

- Introduction to Thermal Properties of Matter
- Heat and Temperature
- Measurement of Temperature
- Absolute Temperature and Ideal Gas Equation
- Thermal Expansion
- Specific Heat Capacity
- Calorimetry
- Change of State
- Heat Transfer
- Newton’s Law of Cooling

##### Sound

- Introduction to Sound
- Types of Waves
- Common Properties of All Waves
- Transverse Waves and Longitudinal Waves
- Mathematical Expression of a Wave
- The Speed of Travelling Waves
- Principle of Superposition of Waves
- Echo, Reverberation and Acoustics
- Qualities of Sound
- Doppler Effect

##### Optics

- Introduction to Ray Optics
- Nature of Light
- Ray Optics Or Geometrical Optics
- Reflection
- Refraction
- Total Internal Reflection
- Refraction at a Spherical Surface and Lenses
- Dispersion of Light and Prisms
- Some Natural Phenomena Due to Sunlight
- Defects of Lenses (Aberrations of Optical Images)
- Optical Instruments
- Optical Instruments: Simple Microscope
- Optical Instruments: Compound Microscope
- Optical Instruments: Telescope

##### Electrostatics

- Introduction to Electrostatics
- Electric Charges
- Basic Properties of Electric Charge
- Coulomb’s Law - Force Between Two Point Charges
- Principle of Superposition
- Electric Field
- Electric Flux
- Gauss’s Law
- Electric Dipole
- Continuous Distribution of Charges

##### Electric Current Through Conductors

- Electric Current
- Flow of Current Through a Conductor
- Drift Speed
- Ohm's Law (V = IR)
- Limitations of Ohm’s Law
- Electrical Power
- Resistors
- Specific Resistance (Resistivity)
- Variation of Resistance with Temperature
- Electromotive Force (emf)
- Combination of Cells in Series and in Parallel
- Types of Cells
- Combination of Resistors - Series and Parallel

##### Magnetism

- Introduction to Magnetism
- Magnetic Lines of Force and Magnetic Field
- The Bar Magnet
- Gauss' Law of Magnetism
- The Earth’s Magnetism

##### Electromagnetic Waves and Communication System

- EM Wave
- Electromagnetic Spectrum
- Propagation of EM Waves
- Introduction to Communication System
- Modulation

##### Semiconductors

- Introduction to Semiconductors
- Electrical Conduction in Solids
- Band Theory of Solids
- Intrinsic Semiconductor
- Extrinsic Semiconductor
- p-n Junction
- A p-n Junction Diode
- Semiconductor Devices
- Applications of Semiconductors and P-n Junction Diode
- Thermistor

## Centre of Mass:

Centre of mass of a system is the point that behaves as the whole mass of the system is concentrated at it and all external forces are acting on it.

For rigid bodies, the centre of mass is independent of the state of the body, i.e., whether it is in rest or in accelerated motion the centre of mass will remain the same.

## Centre of Mass of System of n Particles

If a system consists of n particles of masses m_{1}, m_{2}, m_{3},… m_{n} having position vectors r_{l}, r_{2}, r_{3},… r_{n}. then position vector of centre of mass of the system, `"r"_("CM") = ("m"_1"r"_1 + "m"_2"r"_2 + "m"_3"r"_3 + ... + "m"_"n" "r"_"n")/("m"_1 + "m"_2 + "m"_3 + ... + "m"_"n") =(sum_(i = 1)^"n" "m"_"i" "r"_"i")/(sum "m"_"i")`

In terms of coordinates,

`x_("CM") = ("m"_1x_1 + "m"_2x_2 + ... +"m"_"n" x_"n")/("m"_1 + "m"_2 + ... +"m"_"n") = (sum_(i = 1)^"n" "m"_ix_i)/(sum "m"_i)`

`"y"_("CM") = ("m"_1"y"_1 + "m"_2"y"_2 + ... +"m"_"n" "y"_"n")/("m"_1 + "m"_2 + ... +"m"_"n") = (sum_(i = 1)^"n" "m"_i"y"_i)/(sum "m"_i)`

`"z"_("CM") = ("m"_1"z"_1 + "m"_2"z"_2 + ... +"m"_"n" "z"_"n")/("m"_1 + "m"_2 + ... +"m"_"n") = (sum_(i = 1)^"n" "m"_i"z"_i)/(sum "m"_i)`

## Centre of Mass of Two Particle System

Choosing O as origin of the coordinate axis.

**(i)** Then, position of centre of mass from `"m"_1 = ("m"_2"d")/("m"_1 + "m"_2)`

**(ii)** Position of centre of mass from `"m"_2 = ("m"_1"d")/("m"_1 +"m"_2)`

**(iii)** If position vectors of particles of masses m_{1} and m_{2} are r_{1} and r_{2}respectively, then

`r_(CM) = ("m"_1"r"_1 + "m"_2"r"_2)/("m"_1 +"m"_2)`

**(iv)** If in a two particle system, particles of masses m_{1} and m_{2 }moving with velocities v_{1 }and v_{2 }respectively, then velocity the centre of mass.

`"V"_("CM") = ("m"_1"v"_1 + "m"_2"v"_2)/("m"_1 +"m"_2)`

**(v)** If accelerations of the particles are a_{1}, and a_{2} respectively, then acceleration of the centre of mass.

`a_(CM) = ("m"_1"a"_1 + "m"_2"a"_1)/("m"_1 + "m"_2)`

**(vi)** Centre of mass of an isolated system has a constant velocity.

**(vii)** It means an isolated system will remain at rest if it is initially rested, or will move with a same velocity if it is in motion initially.

**(viii)** The position of centre of mass depends upon the shape, size and distribution of the mass of the body.

**(ix)** The centre of mass of an object need not lie with in the object.

**(x)** In symmetrical bodies having homogeneous distribution of mass, the centre of mass coincides with the geometrical centre of the body.

**(xi)** The position of centre of mass of an object changes in translational motion, but remains unchanged in rotatory motion.