Arihant MagBook General Science PDF

Coverage of Important Facts from NCERT Books (Class 6-12) A Must for Civil Services (Pre) Examination, State PCS & Other Competitive Exams GENERAL SCIENCE Coverage of Important Facts from NCERT Books (Class 6-12) Authored By Poonam Singh, Mansi G...

Coverage of Important Facts from NCERT Books (Class 6-12) A Must for Civil Services (Pre) Examination, State PCS & Other Competitive Exams GENERAL SCIENCE Coverage of Important Facts from NCERT Books (Class 6-12) Authored By Poonam Singh, Mansi Garg ARIHANT PUBLICATIONS (India) LTD. All Rights Reserved © PUBLISHER No part of this publication may be re-produced, stored in a retrieval system or by any means, electronic, mechanical, photocopying, recording, scanning, web or otherwise without the written permission of the publisher. Arihant has obtained all the information in this book from the sources believed to be reliable and true. However, Arihant or its editors or authors or illustrators don’t take any responsibility for the absolute accuracy of any information published and the damage or loss suffered thereupon. All disputes subject to Meerut (UP) jurisdiction only. ADMINISTRATIVE & PRODUCTION OFFICES Regd. Office 'Ramchhaya' 4577/15, Agarwal Road, Darya Ganj, New Delhi -110002 Tele: 011- 47630600, 43518550 Head Office Kalindi, TP Nagar, Meerut (UP) - 250002, Tel: 0121-7156203, 7156204 SALES & SUPPORT OFFICES Agra, Ahmedabad, Bengaluru, Bareilly, Chennai, Delhi, Guwahati, Hyderabad, Jaipur, Jhansi, Kolkata, Lucknow, Nagpur & Pune. ISBN 978-93-25798-08-3 PO No : TXT-XX-XXXXXXX-X-XX PRODUCTION TEAM Publishing Managers : Amit Verma Inner Designer : Mazher Chaudhary Project Head : Karishma Yadav Page Layouting : Sundar Bisht Project Coordiantor : Shivam Gupta Proof Reader : Sundip Giri Cover Designer : Bilal Hashmi Published By Arihant Publications (India) Ltd. For further information about the books published by Arihant, log on to www.arihantbooks.com or e-mail at [email protected] Follow us on PHYSICS CHEMISTRY 1. Mechanics 1-12 1. General Chemistry 54-58 Physical Quantity Matter Dimensions Solid Kinematics Liquid Force Gas Work, Energy and Power Substances Collision Elements Moment of Inertia Compounds Gravitation Mixtures Planets Solution Satellite Colloids Around Us 2. Properties of Matter 13-18 2. Atomic Structure and Chemical Matter Bonding 59-65 Solid Atoms and Molecules Fluid Atomic Models Bernoulli’s Theorem Planck’s Quantum Theory Shell 3. Oscillations and Waves 19-24 Quantum Numbers Periodic Motion Pauli’s Exclusion Principle Wave Radioactivity Sound Soddy Fajan’s Group Displacement Law Sonar Applications of Radioactivity and Radioisotopes 4. Heat and Its Transmission 25-29 Nuclear Hazards and Safety Measures Heat Chemical Bonding Temperature 3. Classification of Elements 66-69 Calorimetry Evolution of Periodic Table Thermodynamics Hydrogen Black body 4. Chemical Reactions and Equations 70-74 5. Optics 30-37 Physical and Chemical Change Light Chemical Reactions Mirrors Oxidation and Reduction Lenses Electrolysis Batteries 6. Electricity and Magnetism 38-45 Enzyme Catalysis Electricity 5. Elements and Compounds 75-85 Magnetism Metals 7. Modern Physics 46-53 Metallurgy Atom Non-Metals Electronics Metalloids Universe Acid and Base Salts  6. Organic Chemistry 86-94 Excretion in Humans Organic Compounds Skeletal System Bioactive Compounds Neural Coordination in Humans Coal Sense Organs Petroleum Chemical coordination by Endocrine System Fuels 5. Plant Physiology 144-147 7. Environmental Chemistry 95-100 Nutrition in Plants Environment Respiration in Plants Atmospheric Pollution Transportation in Plants Water Pollution Excretion in Plants Soil Pollution Mineral Nutrition in Plants 8. Chemistry In Everyday Life 101-109 Plants Growth and Development Synthetic Materials 6. Reproduction in Plants and Chemicals in Agriculture Animals (Humans) 148-153 Chemicals in Medicines Reproduction Chemicals in Food Reproductive Health Fire Extinguisher Sexually Transmitted Diseases (STDs) Chemicals in Cosmetics 7. Genetics and Evolution 154-159 BIOLOGY Genetics Sex Determination in Humans 1. Cell Biology 110-116 Gene and Gene Concept Biology: An Introduction Evolution The Cell Biomolecules 8. Ecology 160-162 2. Biological Classification 117-126 9. Biology in Human Welfare 163-171 Classification of Living Organisms Agriculture Systems of Classification Animal Husbandry Viral Diseases of Human Beings Plant Breeding Vaccination 3. Structural Organisation of Plants and Animals 127-133 SCIENCE & TECHNOLOGY Morphology of Plants 1. Computer and Information Anatomy of Plants Technology 172-181 Wood Computer Anatomy of Animals Hardware Some Specialised Tissue Structures of Animals Software 4. Human Physiology 134-143 Cyber Crimes Nutrition in Animals Internet Digestion in Humans Artificial Intelligence Respiration in Humans Robotics In India Transportation in Humans 2. Telecommunication 182-186 5. Indian Nuclear Programme 203-209 Telecommunication Atomic Energy Generation of Mobile Phone Nuclear Reactor/Atomic Reactor Television Development of Nuclear Energy in India Radio Isotopes 3. Biotechnology 187-194 Nuclear Waste Management Microorganisms DNA Profiling/Sequencing 6. Indian Defence Programme 210-216 Human Genome Project (HGP) DRDO Genetic Engineering Types of Missile Genetically Modified Organism (GMO) Radar Systems Tissue Culture Indian Navy Ships Aircrafts 4. Indian Space Programme 195-202 ISRO Appendix 217-222 Indian Remote Sensing Satellite System Some Early Satellites Practice Sets (1-5) 223-246 Prominent Space Missions of India Previous Years’ Solved Papers Set 1 247-257 Satellite Launch Pads All Over the World Previous Years’ Solved Papers Set 2 258-264 Major Space Missions TOPICS FOCUS & TREND OF QUESTIONS Electricity and Magnetism PHYSICS Significant topics in this chapter are electric field, Mechanics capacitor, resistance, conductors and semiconductors, The important topics in this chapter are fundamental electric cell, magnetism and earth’s magnetic field, units and dimensions, various types of weak and strong ferromagnetism and electro magnetic induction, forces, newton's law of motion and inertia, different working principles of transformer and dynamo. types of energy and conservation of energy, mass and Questions have asked recurrently on above topics in weight, planets and satellites. Questions asked in previous year’s examinations. previous exams are related to concepts such as force, energy, circular motion of satellites, escape velocity etc. Modern Physics Important topics in this chapter are nuclear fission and Properties of Matter fusion, radioactive decay, photoelectric effect, From examination point of view significant topics are electromagnetic waves and devices based on stress, strain, elasticity, surface tension, capillarity, electromagnetic radiations, electronics, nano viscosity, stoke's law and bernoulli's theorem. Most of technology, radar and Solar system. Previous exam the questions asked in previous exams from this section questions were based on process involved in nuclear arere garding elastic limit, fracture point, capillary action reactors, nuclear forces, devices based on photoelectric and viscous flow. effect and properties of comets, asteroids and meteors in Oscillations and Waves solar system. This chapter deal with important topics such as oscillatory motion including SHM and wave motion, speed, characteristics, properties of sound wave CHEMISTRY including doppler’s effect. Previous year's exam General Chemistry questions were based on amplitude and wavelength of This chapter will introduce the reader to the chemistry wave motion as well as reflection, refraction and and matter concepts related to classification of matter, diffraction of sound waves. solution, colloids and suspensions are important from examination point of view since questions have been Heat and Its Transmission asked in the past about it. Important topics are various scales of temperature measurement, laws of thermodynamics, specific and Atomic Structure and Chemical Bonding latent heat, humidity, convection, conduction and This chapter discusses vital topics like atoms, molecules, radiation and properties of black body. Questions were subatomic particles, and bonds. From an examination asked on various mode of transmission of heat and point of view the topics of carbon dating, geological specific and latent heat. dating, electrovalent, covalent and van der waals forces Optics are important. The concepts related to valency are also This is the most important chapter from the perspective very important. of competitive examination. Important topics from Classification of Elements examination point of view are light and related This chapter presents the concepts related to the properties of reflection, refraction and total internal periodic table. From examination point of view the new reflection, properties of concave, convex and spherical super heavy element unseptium, and various blocks of mirrors, lenses, behaviour of prism, dispersion, scattering periodic table and periodic properties are important. and interference of light.  Chemical Reactions and Equations Structural Organisation of Plants and Animals This chapter discusses the types of chemical reactions, Concepts of xylem and phloem, meristmatic tissues, catalysts and batteries. Questions relating to oxidation sapwood and hardwood, types of tissues, blood are not and reduction fuel cells can appear in the exam. only interesting but also important. From exam perspective, questions relating to blood groups – the Elements and Compounds antigens, antibodies and donor groups appear very This chapter discusses important metals, non-metals and frequently. their properties. It also discusses concepts relating to acids, bases and salts. From examination point of view, Human Physiology all the toxic materials and nutrition related materials are Concepts relating to digestive system, respiratory important. system, cardiovascular, neural, endocrinal and excretory system are the most important. From the examination Organic Chemistry perspective, questions can primarily be asked regarding This chapter introduces the reader to various organic the role of various vitamins, importance of proteins, compounds and fuels. From examination point of various disorders associated with various systems, tables view –fuels, hydrocarbons and petroleum are extremely related to various glands are extremely important. important. Nutrition itself is one of the most important topics for Environmental Chemistry preliminary examination. This is the most important section in Chemistry from Plant Physiology examination point of view as questions are asked in The topics of photosynthesis, mineral nutrition in almost every exam. Some important topics are abiotic, plants are most important. Questions related to xylem, biotic and energy components, different types of phloem transportation and transpiration have appeared pollution and pollutants and pollution control. This in the past. chapter carries nearly as much importance as all other chapters combined in terms of both importance Reproduction in Plants and Humans and relevance. The concepts associated with a sexual and sexual reproduction are important since they help understand Chemistry in Everyday Life various issues related with biology. Questions related to It is important to understand various synthetic sexually transmitted diseases, and reproductive healths materials like cement, glass, fertilizers, pesticides, have been asked in the previous exams. explosives from examination point of view. Operation of fire-extinguisher, various chemicals in Genetics and Evolution medicine, chemicals in food need to be understood One of the most important and interesting topics to thoroughly – since there is great scope for questions understand because it forms the basis for biotechnology, from that section. green revolution and other associated topics. From exam point of view, the concepts of recessive allele, mendels laws, theory of evolution and genetic disorders are BIOLOGY important. Cell Biology Ecology Some important topics are cell cycle and cell division, This chapter introduces the reader to ecology – from a enzymes and inhibitors. Most of the questions which biological and terminological perspective. were asked in past were related to mitosis, meosis, Understanding these terms are important not only to enzymes and inhibitors. gain a grasp on the environment and biodiversity subject in syllabus, but also because questions related to Biological Classification them can appear directly in the exam. The concepts related to bacteria, virus, protozoa are very important – especially to understand more advanced Biology in Human Welfare concepts in biotechnology, pathology etc. Questions The concepts related to economically important plants, relating to gram staining, modes of transmission can be biofertilizers and vaccination are important from asked in the exam. examination point of view. Questions have been asked in the past about Principal Vaccines.  regarding the developments in Indian space SCIENCE AND TECHNOLOGY programme. Some of the important topics from Computer and Information Technology examination point of view are INSAT, IRS, various In almost all the competitive examinations questions space launching stations of India and world, types are asked frequently from this section. Some of the of launch vehicles used in India, IRNSS, GPS, glonass, important topics are types of computers, super galileo, GIS, various space missions of India, cryogenic computers in India and world, input and output technology, international space mission etc. devices, types of memory, software, types of network, cyber crimes etc. Indian Nuclear Programme This is one of the most important topics from which Telecommunication questions are asked on regular basis regarding the Questions are asked from this topic in all exams latest developments in the field of nuclear regarding the current developments in the technology and the basic concepts of nuclear telecommunication technology. Some of the technology. Some of the important topics from important topics from examination perspective are examination perspective are various parts of a optical fibre, wireless communication, mobile nuclear reactor and their functions, types of nuclear operating systems, GPRS, types of television etc. reactors used in India, India’s important nuclear Biotechnology installations and their location along with the types Biotechnology is one of the hot topics now-a-days, of fuel used, various applications of radio isotopes, from which questions are asked in most of the radioactive wastes etc. competitive examinations. mportant topics from Indian Defence Programme examination perspective are uses of biotechnology, In almost all the competitive examinations questions genetic engineering, cloning, genetically modified are asked regarding latest developments in the crops (Bt brinjal), biodiesel etc. Indian Defence system. Some of the important topics Indian Space Programme are types of missiles inducted in Indian defence After analysing question papers of various forces, range of missiles, types of radars, naval ships, examinations, it has been found that questions are submarines, tanks, aircrafts etc. asked in most of the competitive examinations  Physics Chapter one Mechanics Physical Quantity Mechanics is the branch — It is a physical property of a body, or substance, or of a phenomenon, that can be quantified by measurement. of science (physics) concerned with the Measurement of a Physical Quantity behaviour of physical — It is done by assigning a value to a physical quantity by comparing it with a standard value (calibrated value) of that physical quantity which is called unit. bodies, when subjected — To know the value (or magnitude) of a physical quantity we generally measure it in to forces or different system of units. displacements, and the Errors in Measurement subsequent effects of — The difference between the true value and the measured value of a quantity is known as the bodies on their error. environment. There are mainly three types of error occurs in measurement. – Absolute Error It is the difference of true value and measured value. – Relative Error It is defined as the ratio of absolute error to mean value. – Percentage Error It is defined as fractional error multiplied by 100. System of Units — Physical quantities are measured in four system of units as below. – CGS (Centimetre, Gram, Second) – FPS (Foot, Pound, Second) – MKS (Metre, Kilogram, Second) – SI system (International System of Units). Fundamental Quantities — The physical quantities which are independent to each other are called fundamental quantities and their units are called fundamental units. — The most accepted one is SI system which was adopted in 1971 by conference of weights and measures held in Geneva. — There are seven fundamental quantities in SI system Fundamental Quantities in SI System S.No. Fundamental quantity Fundamental unit Symbol 1. Length Metre m 2. Mass Kilogram kg 3. Time Second s 4. Electric current Ampere A 5. Temperature Kelvin K 6. Luminous intensity Candela cd 7. Amount of substance Mole mol 2 Magbook ~ General Science — There are also two supplementary fundamental units in SI — Area is related with square of length, some units of area system. are – Radian (rad) It is unit of plane angle. – 1 barn = 10−28 m 2 – Steradian (sr) It is unit of solid angle. – 1 acre = 4047 m 2 – 1 hectare = 104 m 2 Derived Quantities — The physical quantities which are obtained with the help of — Volume is related with cube of length, some units of volume are fundamental quantities are called derived quantities and their 10 millilitre (mL) = 1 centilitre (cL) units are called derived units. For example, Velocity, Force, Work, Density, Momentum etc = 0.018 pint (0.021 US pint) are derived quantities. 100 centilitre (cL) = 1 litre (L) = 1.76 pint 10 litre (L) = 1decalitre (daL) Some Important Derived Units = 2. 2 gallon (2.63 US gallon) Physical quantity Unit (SI) Symbol 1 cubic centimetre (cm 3 ) = 1 millilitre (mL) Force newton N 1 barrel = 159 litre Energy joule J Speed metre/second ms −1 Unit of Mass Angular velocity radian/second rad s −1 — The SI unit of mass is kilogram. One kilogram is Frequency hertz Hz defined as the mass of 5.0188 × 1025 atoms of Moment of inertia kilogram metre square kg m 2 carbon−12. Momentum kilogram metre/second kg ms −1 Other Units of Mass Angular momentum kilogram metre square/second kg m 2 s −1 1 – 1 gram = kg = 10−3 kg Pressure pascal Pa 1000 1 Power watt W – 1 milligram = g = 10−6 kg Surface tension newton per metre Nm −1 1000 – 1 Atomic Mass Unit (amu) = 1.66 × 10−27 kg Viscosity newton second per metre square Nsm −2 Thermal conductivity watt per metre Kelvin Wm −1 K −1 – 1 quintal = 100 kg – 1 tonne or metric ton =1000 kg Electric charge coulomb C – 1 slug = 14.57 kg Potential volt V – 1 Chandra Sekhar Limit (CSL) = 1.4 times the mass of sun Capacitance farad F = 2.8 × 1030 kg Electrical resistance ohm Ω Unit of Time Inductance henry H Magnetic flux weber Wb — The SI unit of time is second. One second is defined 1 Luminous flux lumen lm as part of a mean solar day. 86400 Impulse newton second Ns Other Units of Time Unit of Length – 1 microsecond = 10 −6 s — The SI unit of length is metre (m). One metre is the distance – 1 picosecond = 10−12 s 1 – 1 Lunar month = 295. day travelled by light in vacuum in of a second. 29, 97, 92, 458 – 1 nanosecond = 10−9 s Some Other Units of Length – 1 shake = 10−8 s — Light year The distance travelled by light in one year in Important Prefixes to Units vacuum. peta (P) = 1015 exa (E) = 1018 1 light year = 9.46 × 1015 m giga (G) = 10 9 tera (T) = 1012 — Parsec (Parallactic Second) The distance at which an arc of length equals to one astronomical unit subtends an angle of kilo (K) = 103 mega (M) = 106 one second at a point. deca (da) = 10 hecto (h) = 102 −2 – 1 parsec = 3.085 × 1016 m – 1 micron or µm = 10−6 centi (c) = 10 deci (d) = 10−1 – 1 AV = 1.49 × 1011 m – 1 angstrom or Å = 10−10 m micro = 10−6 milli (m) = 10−3 – 1 nanometre or nm = 10−9 m – X-unit = 10−14 m pico (p) = 10 −12 nano (n) = 10−9 −15 – 1 Fermi = 10 m – 1 yard = 0.9144 m zatto (a) = 10−18 femto(f) = 10−15 Magbook ~ Mechanics 3 Scalar and Vector Quantities Distance and Displacement On the basis of magnitudes and direction, physical quantities — The length of the actual path travelled by an object during are categorised as below motion in a given interval of time is called the distance — Scalars Physical quantities which have only magnitude travelled by the object. and no direction are called scalars quantities e.g., length, — The change in position of the object along a particular mass, time etc. direction in a given interval of time is called the — Vectors Physical quantities which have both magnitude as displacement of the object. well as direction are called vectors quantities e.g., force, — Displacement can be positive, negative or zero but displacement, impulse etc. distance cannot be negative. – A vector obeys triangle law and parallelogram law of addition — Distance is a scalar quantity and displacement is vector of two vectors. Zero vector or null vector, unit vector, etc are quantity. some special types of vectors. — If an object travels equal distances in equal intervals of time, then it is said to be in uniform motion. Dimensions — If an object travels unequal distances in equal intervals of — The dimensions of a physical quantity are the powers to time, then it is said to be in non-uniform motion. which the fundamental units are raised in order to obtain the units of that quantity. Speed — The fundamental quantities mass, length, time, — The distance covered by a moving body in a unit time temperature, luminous intensity, amount of substance and interval is called its speed. current are respectively represented as M, L, T, θ, cd, N Distance travelled and A. Speed = Time taken — The dimension of the physical quantity shall be written in the manner [Ma Lb Tc θd ]. — The speed at an instant of time is known as instantaneous where, a, b, c and d are exponents. speed. — Some Important dimensional Formulae are — An object is said to be moving with uniform speed if it Displacement [L] covers equal distances in equal intervals of time. – Velocity = = = [LT −1 ] Time [T] — An object is said to be moving with non-uniform or – Density = Mass = [M] = [ML −3 ] variable speed if it covers unequal distances in equal Volume [L 3 ] intervals of time. — Average speed of an object is the ratio of the total Kinematics distance travelled to the total time taken to cover this distance. — The branch of Physics which deals with the study of Total distance travelled motion of material objects etc is called mechanics. Average speed = Total time taken Kinematics is a branch of mechanics which deals with the study of motion of the objects without taking into account — When a body travels equal distances with speeds v 1 and the cause of their motion. v 2 , then average speed is the harmonic mean of the two speeds. Rest and Motion 2 1 1 2 v 1v 2 = + ⇒ v = — An object is said to be at rest if it does not change its v v1 v 2 v1 + v 2 position with respect to its surroundings with time and said to be in motion if it changes its position with respect — When a body travels for equal times with speeds v 1 and v 2 , to its surroundings with time. then average speed is the arithmetic mean of the two speeds. — Basic types of motion are v +v 2 – Rectilinear motion The motion in which particle moves along v = 1 a straight line, such as moving car on horizontal road, motion 2 under gravity etc. Velocity – Angular motion The motion in which particle moves along a — The time rate of change of displacement of a body is curved track, such as particle going on a circle, projectile motion, rotation of machine shaft etc. called its velocity. – Rotational motion If a body rotates about a given axis, its Displacement Velocity = motion is called rotational motion, such as motion of a fan. Time 4 Magbook ~ General Science — The velocity at an instant of time is known as Equations of Uniformly Accelerated Motion instantaneous velocity. (Along straight line) — An object is said to be moving with uniform velocity if it undergoes equal displacements in equal intervals of time. — If a body started its motion with initial velocity u and attains final velocity v in time interval t. The acceleration assumed to — An object is said to be moving with non-uniform or variable be uniform in motion is a and the distance travelled is s, then velocity if it undergoes unequal displacements in equal equations of motion intervals of time. v = u + at — Average velocity of an object is the ratio of the total 1 displacement to the total time taken. s = ut + at 2 2 Total displacement v 2 = u 2 + 2as Average velocity = Total time taken — If any body is falling freely under gravity, then a is replaced by g in above equations. Relative Velocity — If an object is thrown vertically upward, then in above Relative velocity of an object with respect to another object is equations of motion a is replaced by ( − g ). the time rate of change of position of one object with respect — Distance travelled by a body in a particular nth second is to another object. If two objects A and B are moving with a velocities v A and v B making an angle θ with each other, then given by sn = u + (2n − 1) 2 magnitude of relative velocity of A with respect to B is given by — For a body with zero acceleration or constant speed, graph between velocity and time will be a line parallel to time axis vAB –vB and for accelerating or decelerating body the graph will be θ 0− a straight line inclined to time axis and velocity axis. α 18 θ — Graph between position (distance)-time for an accelerating or vA decelerating body is always a parabola whereas v AB = v A − v B acceleration-time graph for uniformly accelerating body is a line parallel to time axis. | v AB | = v 2A + v 2B − 2v A v B cos θ — In case of uniform accelerated, the graph between position If v AB makes an angle α with v A , then and velocity is always parabola. v B sinθ In case of uniformly accelerated motion, the graph between tan α = — v A + v AB cos θ velocity and time is always a straight line. If both objects are moving in same direction (i.e. θ = 0°), then — Slope of displacement-time graph gives velocity and slope v AB = v A − v B of velocity-time graph gives acceleration. If both objects are moving in opposite directions (i.e. θ = 180° ), then Projectile Motion v AB = v A + v B — When a body is thrown from horizontal making an angle (θ ) except 90° , then its motion under gravity is a curved parabolic path, called trajectory and its motion is called Acceleration projectile motion. y — The time rate of change of velocity of a body is called its acceleration. u u cos θ Trajectory Change in velocity (parabolic) Acceleration = u sin θ H Time taken θ u′ −2 — It is a vector quantity and its SI unit is ms. O u cos θ A x R — Acceleration at an instant of time is known as instantaneous acceleration. — The horizontal component of velocity (u cos θ ) of projectile is responsible for its horizontal motion and remains — When the velocity of a body increases with time, then its constant and vertical component of velocity (u sin θ ) is acceleration is positive and if velocity decreases with responsible for its vertical motion. time, then its acceleration is negative called deceleration or retardation. For examples — If acceleration does not change with time, it is said to be – The motion of a bullet shot from the gun constant acceleration. – The motion of a rocket after burn-out – The motion of a bomb dropped from a aeroplane etc. Magbook ~ Mechanics 5 Some terms related with the projectile motion are Angular Displacement and Velocity — Time of flight (T ) It is the time taken by the projectile to — The angle subtended at the centre cover the journey from point of projections (O) to end point of a circle by a body moving along ∆S ( A ). the circumference of the circle is θ 2 u sin θ called angular displacement of the O r It is given by T = g body. Its unit is radian (rad). where, g is acceleration due to gravity. Maximum Height (H) It is the maximum height attained by Length of the arc ∆s Angular displacement (θ ) = = — the projectile during the journey from ‘‘O’’ to “A” as shown Radius of the circle r in the diagram. — The time rate of change of angular displacement is called u 2 sin2 θ angular velocity. Its unit is rad s−1. It is given by H = 2g Angular displacement ∆θ Angular velocity (ω ) = = — Range (R ) It is the distance between starting point (O ) and Time ∆t final point ( A ). — If time period of uniform circular motion is T, then average u 2 sin 2θ angular velocity is given by It is given by R= g 2π  1  ω= = 2πf where, Frequency (f ) =  T  Time period (T )  Properties of Projectile Motion — Horizontal range is maximum when angle of projection is — Linear velocity in circular motion is given by 45°. Horizontal range is same for angle of projections θ° Linear velocity = Angular velocity × radius and ( 90 − θ )°. or v = ω × r — The horizontal component of velocity remains unchanged Centripetal Acceleration during the projectile motion. At the highest point of projectile motion, the direction of motion becomes — During circular motion an acceleration acts on the body horizontal as vertical component of velocity becomes zero towards the centre, called centripetal acceleration. at that point. v2 — Centripetal acceleration (ac ) = = rω 2 — If we drop down a ball from a height and at the same time r thrown another ball in a horizontal direction, then both the where, v = uniform speed of the body balls would strike the earth simultaneously at different r = radius of circular path and places. ω = angular velocity. — The direction of centripetal acceleration is always towards Circular Motion the centre of the circular path. — The motion of an object along a circular path is called circular motion. Force v A v — It is an external push or pull which can change or tries to change the state of rest or of uniform motion. SI unit is newton (N) and CGS unit is dyne. 1 N = 105 dyne. — If sum of all the forces acting on a body is zero, then body O is said to be in equilibrium. — In nature, there are four basic types of forces – Gravitational force – Electromagnetic force v – Weak nuclear force – Strong nuclear force v — Among these forces, the strong nuclear force is strongest one. — Circular motion with a constant speed is called uniform circular motion. Centripetal Force — The direction of motion at any point in circular motion is — During circular motion a force always acts on the body given by the tangent to the circle at that point. towards the centre of the circular path, called centripetal — In uniform circular motion, the velocity and acceleration force. both changes. mv 2 Centripetal force (F ) = = mrω 2 — In case of non-uniform circular motion, the speed r changes from point to point on the circular track. where, m = mass of the body. 6 Magbook ~ General Science Centrifugal Force Inertia of Rest — In circular motion we experience that a force is acting on — It is the property of a body by virtue of which it cannot us in opposite to the direction of centripetal force called change its state of rest on its own. centrifugal force. This is an apparent force or imaginary – When a bus or train at rest starts, to move suddenly, the force and also called a pseudo force. passengers sitting in it jerk in backward direction due to their inertia of rest. Applications of centripetal and centrifugal forces – The dust particles come out from a carpet when it is beaten — Cyclist inclined itself from vertical to obtain required with a stick due to their inertia of rest. centripetal force. To take a safe turn cyclist slower down – A passenger jumping out from a rapidly moving bus or train his speed and moves on a path of larger radius, to balance is advised to jump in forward direction and run forward for a short mile due to inertia of rest. decreased value of friction due to bending. — Roads are banked at turns to provide required centripetal Inertia of Motion force for taking a turn. The component of normal reaction — It is the property of a body by virtue of which it cannot force provides required centripetal force. change its state of uniform motion on its own. — For taking turn on a curved road, the frictional force is — When a running bus or train stops suddenly, the acting between the tyres of the vehicle and the road acts passengers sitting in it jerk in forward direction due to as centripetal force. inertia of motion. — If a car takes a turn with a speed greater than the safe limit, then inner tyres leave the roads first in turning of car Momentum because inner tyres were moving in smaller radius, hence The momentum of a moving body is equal to the product of its larger centrifugal force were acting on these tyres so more mass and its velocity. chances of skidding. Its unit is kg - ms −1. It is a vector quantity and its direction is in — If a bucket containing water is revolved fast in a vertical the direction of velocity of the body. plane, the water may not fall even when bucket is Momentum = Mass × velocity completely inverted because a centrifugal force equal or greater than the weight of water pushes the water to the p=m×v bottom of the bucket. Conservation of Linear Momentum — For orbital motion of electrons around the nucleus, The linear momentum of a system of particles remains electrostatic force of attraction is acting between the conserved if the external force acting on the system is electrons and the nucleus as centripetal force. zero. Rocket propulsion and engine of jet aeroplane works on principle of conservation of linear momentum. In rocket, — Cream is separated from milk when it is rotated in a vessel ejecting gas exerts a forward force which helps in accelerating about the same axis. During rotation lighter particles of cream the rocket upward. experience a lesser force than the heavier particles of milk. Therefore, lighter particles tend to adopt a path of smaller Conservation of Angular Momentum radius and move towards the centre. The heavier particles If external torque on a system is zero, angular momentum will tend to adopt a path of larger radius and move towards the remain conserve. It is known as principle of conservation of circumference and hence cream is separated from milk. angular momentum. — For revolution of the earth around the sun, gravitational force of attraction between the earth and the sun acts as centripetal Newton’s Second Law force. — The rate of change of momentum of a body is directly — Torque or Moment of a Force It is the product of the force proportional to the force applied on it and change in and the perpendicular distance of the force from the axis of momentum takes place in the direction of applied force. rotation. It produces rotational effect. It is a vector quantity. ∆p m∆v F = = = ma ∆t ∆t Newton’s Laws where, m is mass of the body and is constant. Newton’s First Law — If the resultant force on a body is zero, the body is said — A body continues in its state of rest or of uniform motion in to be in equilibrium. a straight line unless an external force acts on it. It is Newton’s Third Law based on law of inertia. — For every action, there is an equal and opposite reaction — Inertia is the property of a body by virtue of which it and both act on two different objects. opposes any change in its state of rest or of uniform motion — Rocket is propelled by the principle of Newton’s third law in a straight line. of motion. Magbook ~ Mechanics 7 Rolling friction is lesser than sliding friction. Therefore, it Impulse — is easier to roll a body than to slide it. — A large force which acts on a body for a very short interval — It is easier to drive a bicycle when its tyres are fully of time and produces a large change in its momentum is inflated because it decreases rolling friction. called an impulsive force. — Velocity of the point of contact of the wheel with respect — The impulse of a force acting on a body is equal to the to the floor remains zero all the time while the centre of product of the large force and small time interval for which the wheel moves forward in rolling motion. it acts on a body. — The limiting frictional force is independent of the area of Impulse (I ) = Force × time contact but depends on the nature of the material of the — Its unit is newton-second. surfaces in contact and their roughness or smoothness. — Impulse of a force applied on a body is equal to the — The ratio of limiting friction (F) to the normal reaction (R) change in linear momentum of that body. is called coefficient of friction (µ ) between two surfaces. Impulse = Force × time = Change in momentum F Coefficient of friction (µ ) = Change in momentum R or Force = Time — The angle between the normal reaction (R) and the – A fielder lowers its hand when catching a cricket ball because resultant of limiting friction (F) is called angle of friction by lowering his hands, he increases the time of contact for (θ). stopping the ball and therefore fielder has to apply lesser force F to stop the ball. The ball will also exert lesser force on the where, tan θ = = µ hands of the fielder and the fielder will not get hurt. R – Wagons of a train are provided with the buffers to increase the time of impact during jerks and therefore, decreases the Application of Friction damage. The vehicles like scooter, car, bus, truck etc. are — A ball bearing is a type of rolling-element that uses balls provided with shockers. to maintain the separation between the bearing races as shown in the diagram. The Friction purpose of a ball bearing is to Bearing Races — Friction is a force which opposes the relative motion of the reduce rotational friction and to two bodies when one body actually moves or tries to move support loads (weight). It is over the surface of another body. possible by using atleast two races to contain the balls and — The cause of friction is the strong atomic or molecular transmit the loads through the forces of attraction acting on the two surfaces at the point balls. Balls of actual contact. — In most of the applications one race is stationary and the Types of Friction other is attached to the rotating assembly (e.g. hub or — Static friction The opposing force that comes into play shaft). As one of the bearing races rotates it causes the when one body tends to move over the surface of another balls to rotate as well. Because the balls are rolling they body but the actual motion has yet not started is called have a much lower coefficient of friction than if two flat static friction. Static friction is a self-adjusting force and it surfaces were sliding against each other. Hence, ball adjusts itself so that it becomes equal to the applied force. bearing also minimises the energy loss due to wear and — Limiting friction The maximum static frictional force tear caused by friction. which comes into play, when one body is just at the verge — Friction is necessary for walking, to apply brakes in of moving over the surface of the another body. vehicles, for holding nuts and bolts in a machinery etc. Limiting friction (fs ) = µs R = µsmg — Friction can be decreased by polishing the surfaces by where, µs = coefficient of limiting friction. using lubricants or by using ball bearings. — Kinetic friction The opposing force that comes into play — Tyres are made of synthetic rubber because its coefficient when one body actually moves over the surface of another of friction with road is larger and therefore, large force of body, is called kinetic friction. friction acts on it, which stops sliding at turns. Kinetic friction is of two types — The tyres are threading which also increases the friction – Sliding friction It comes into play when one body slides over between the tyres and the road. the surface of the another body. — When pedal is applied to a bicycle, the force of friction on – Rolling friction It comes into play when one body rolls over rear wheel is in forward direction and on front wheel is in the surface of the another body. the backward direction. 8 Magbook ~ General Science — If a coolie is carrying a load on his head and moving on a Lever horizontal platform, then work done by force of gravity is It is a simple machine in which a straight or inclined rod is made zero as displacement is perpendicular to the direction of to turn or rotate at a point freely or independently. There are force of gravity. three points related to lever namely load, effort and fulcrum. Load The weight carried by the lever is called load. Energy Effort To operate lever, the force applied externally is called — Energy of a body is its capacity of doing work. It is a effort. scalar quantity and its SI unit is joule. Fulcrum The fixed point about which the rod of lever moves M Energy can be transformed into work and vice-versa with the independently is called fulcrum. help of some mechanical device. There are two types of Mechanical Energy, which are as Work, Energy and Power follows Kinetic Energy Work — The energy possessed by a body by virtue of its motion is — Work done by a constant force (F) is equal to the dot called its kinetic energy. product of the force applied on a body and the displacement (s) of the body. — Kinetic energy of the body of mass m moving with velocity 1 p2 W = F ⋅ s = Fs cos θ v is given by K = mv 2 = 2 2m where, θ is the angle between F and s. where, p = mv = momentum of the body. — Work is a scalar quantity. Its SI unit is joule and CGS unit is erg. 1 joule = 107 erg. Potential Energy — Work done by a force is positive if angle between F and s — The energy possessed by any object by virtue of its position is acute angle and negative if angle θ is obtuse angle. or configuration is called its potential energy. — Work done by a force is zero when — Gravitational potential energy, U = mgh – Body is not displaced actually, i.e. s = 0 where, m = mass of the body – Body is displaced perpendicular to the direction of force i.e. g = acceleration due to gravity and θ = 90°. h = height through which body is lifted. Work done by a variable force Different Forms of Energy — Work done by a force is equal to the area under the Solar Energy force-displacement graph, along with proper sign and is — It is the emission of energy by the sun, used in solar given by W = ∫ F ⋅ d s cooker, solar water heater, solar cell etc. Others are Fossil energy, Wind energy, Hydroelectric energy, Nuclear B Energy. A Fossil Energy — Fossil fuels are non-renewable sources of energy such as Force anaerobic decomposition of buried dead organisms. Fossil fuels contain coal, petroleum and natural gas. D C Hydroelectric Energy Displacement — The production of electrical power through the use of the — Work done by force = Area ABCDA gravitational force of falling or flowing water. In our — If we throw a ball upward, work done against gravity is country, more than 23% of water is used in production of given by, W = mgh hydroelectric power. where, m = mass of the body, Nuclear Energy g = acceleration due to gravity and — It is found that when U235 nucleus break-up into lighter h = height through which the ball is raised. nuclei on being bombardment by slow moving neutron, a — The centripetal force acts on a body perpendicular to the large amount of energy released is called nuclear energy. direction of motion. Therefore, work done by or against Nuclear reactors and nuclear bombs are the sources of centripetal force in circular motion is zero. nuclear energy. Magbook ~ Mechanics 9 — If after collision two colliding bodies gets sticked with each Einstein’s Mass-Energy Relation other and moves with a common velocity, then collision is ◆ According to this relation, the mass can be transformed into said to be perfectly inelastic. energy and vice-versa. — In perfectly inelastic collision, the loss of kinetic energy during ◆ When ∆m mass is disappeared, then produced energy collision do not recover at all and two bodies stick together after collision. E = ∆mc 2 where, c = speed of light in vacuum. Centre of Mass — Every physical system of particles (body) is associated Conservative and with a certain point whose motion is characterised by the Non-conservative forces system as a whole, and when a system moves under an external force, then this point moves in a similar way as a — Conservative forces are non-dissipative forces like single particle moves under the same external force. gravitational force, electrostatic force etc. This is called centre of mass of the system. For uniform — For the conservative forces, work done during a round trip rod and solid spherical body, it is at the geometrical is always zero. centre. — Non-conservative forces are dissipative in nature like frictional force, viscous force etc. Moment of Inertia Law of Conservation of Energy — Moment of Inertia of a body with respect to axis of rotation — Energy can neither be created nor be destroyed, only one is the summation of product of the masses of its particles type of energy can be transformed into other form of and square of respective distances from axis of rotation. energy. — Only for conservative forces, (total mechanical energy) Definitions Related to Moment of Inertia initially = (total mechanical energy) finally — Radius of Gyration Radius of gyration is defined as the distance of a point from axis of rotation at which the total Power mass of the body is supposed to be concentrated, such that its moment of inertia would be same. — The rate of doing work by a body is called its power. Work done W F. s I = MK 2 Power = ;P = = = F. v = Fv cosθ Time taken t t — Theorem of Parallel Axes Moment of inertia about any where, θ is the angle between F and v. parallel axis will be sum of moment of inertia about centre of mass and product of mass and square of distance — It is a scalar quantity and its SI unit is joule second − 1 or between the two axes. watt. — Theorem of Perpendicular Axes For a laminar body, — Other units are kilowatt and horse power. moment of inertia about perpendicular axis will be the 1 kilowatt = 1000 W and 1 HP = 746 W sum of moments of inertia about two other mutually perpendicular axes. Collision — Collision between two or more particles is the interaction Gravitation for a very short interval of time in which they apply — Each and every massive body attracts each other by virtue relatively strong forces on each other. of their masses. This phenomenon is called gravitation. — For a collision, physical contact of two bodies is not Newton’s Law of Gravitation necessary. — The gravitational force acting between two point objects is — A collision in which momentum of the system as well as directly proportional to the product of their masses and kinetic energy of the system remains conserved, is called an inversely proportional to the square of the distance elastic collision. between them. — In an elastic collision, all involved forces are conservative Gm1m2 forces. Gravitational force (F) = r2 — A collision in which only momentum remains conserved where, G is universal gravitational constant. but kinetic energy of the system does not remain Its value is 6.67 × 10−11 N -m 2 kg −2. conserved, is called an inelastic collision. — Gravitational force is a central as well as conservative force. 10 Magbook ~ General Science Acceleration Due to Gravity of Earth Mass and Weight — The uniform acceleration produced in a freely falling — The mass of a body is the quantity of matter contained in it. body due to the earth’s gravitational pull, is called It is a scalar quantity and its SI unit is kg. GM acceleration due to gravity, g = 2 — Mass is measured by an ordinary equal arm balance. R where, M = mass of the earth , R = radius of the earth. — Mass of a body does not change from place to place and — The value of g changes slightly from place to place but remains constant. its value near the earth’s surface is 9.8 ms −2. — The weight of a body is the force with which it is attracted — Gravitational force is the weakest force in nature. It is towards the centre of the earth. Weight of a body (w) = mg 1036 times smaller than electrostatic force and 1038 — The centre of gravity of a body is that point at which the times smaller than nuclear force. whole weight of the body appears to act. — The centre of gravity of a body can be inside the material of Factors Affecting Acceleration due to the body or outside it. For regularly shaped body, the centre Gravity of gravity lies at its geometrical centre. — Shape of Earth Earth is not completely spherical its — It is a vector quantity and its SI unit is newton (N). It is radius at equator is approximately 42 km greater than measured by a spring balance. its radius at poles. — Weight of a body is not constant, it changes from place to — The value of g is maximum at poles and minimum at place. equator. The difference in value of g at poles and at equator is 3.4 cms−2. Weight of a Body in a Lift — Rotation of Earth about its Own Axis If ω is the angular — When lift is at rest or in uniform motion The weight velocity of rotation of earth about its own axis, then recorded in spring balance (i.e. apparent weight) is equal to acceleration due to gravity at any place on the earth is the real weight of the body w = mg. given by g ′ = g − Rω 2 cos2 λ — When lift is accelerating upward The weight recorded in where, λ = latitude of the place, R = radius of the earth. spring balance is greater than the real weight of the body At poles, λ = 90° and at equator λ = 0° Therefore, there w ′ = m( g + a ) is no effect of rotation of the earth at poles and — When lift is accelerating downward The weight recorded in maximum at equator. spring balance is lesser than the real weight of the body. w ′ = m( g − a ). — Effect of Altitude The value of g at height h from the earth’s surface is given by — When lift is falling freely under gravity The apparent weight of the body g  2 h g′ = ≈ g 1 −  if h < < R w′ = m (g − g ) (Qa = g )  h 2  R   1 +  w′ = 0  R Therefore, body will experiences weightlessness. Therefore, g decreases with altitude. Weight of a Body at the Moon — Effect of Depth The value of g at depth from the earth’s — As mass and radius of moon is lesser than the earth, so the  h surface is given by g ′ = g 1 −  force of gravity at the moon is also less than that of the  R g earth. It’s value at the moon’s surface is. Therefore, g decreases with depth and becomes zero at 6 centre of the earth. Planets Gravitational Field and Potential — The heavenly bodies which revolve around the sun are — Gravitational Field The space surrounding the material called planets. body in which its gravitational force can be experienced. — Our solar system contains eight planets (as Pluto has lost its — Gravitational Potential It is the work done in carrying planet status, now it is considered as a dwarf planet). The unit mass from infinity to a particular point in the field. order of the planets in the solar system with their increasing — Gravitational Potential Energy It is the work done in distance from the sun is assembling system of masses from infinity to its present 1. Mercury, 2. Venus, 3. Earth, 4. Mars, configuration. 5. Jupiter, 6. Saturn, 7. Uranus, 8. Neptune. Magbook ~ Mechanics 11 Weather monitoring which is predicted on the basis of Kepler’s Laws of Planetary — information about moisture present in air, atmospheric Motion pressure etc, obtained through a polar satellite. Kepler’s Three Laws are — We are able to see a live telecast of cricket world cup – All planets revolve around the sun in elliptical orbits with the match or other programme with the help of a sun at its one focus. communication satellite which is a geostationary satellite. – The areal speed of a planet around the sun is constant. – The square of the time period (T ) of revolution of a planet Time Period of a Satellite around the sun is directly proportional to the cube of the — It is the time taken by a satellite to complete one revolution. semi-major axis (a) of its elliptical orbit, i.e. T 2 ∝ a 3. R If satellite is near the earth’s surface, then T = 2 π ≈ g Satellite 84.6 min — A heavenly body revolving around a planet in an orbit is called a satellite. Moon is a natural satellite of the earth. The satellite may be artificial. Artificial satellites are of two Escape Velocity types The minimum velocity with which when an object is thrown vertically upwards from the earth’s surface just crosses the Geostationary Satellites earth’s gravitational field and never returns. Escape velocity (v e ) — It revolves around the earth in equatorial orbits which is 2 GM also called Geostationary or Geosynchronous orbit at a = = 2gR R height of approximately 36000 km above the earth’s Its value on earth’s surface is 11.2 km/s. surface. The time period of these satellites is 24 hour exactly equal to the time period of earth’s rotation about Escape velocity = 2 (orbital speed of a satellite when it is near its own axis. the earth’s surface) v e = 2 v o — These satellites appear stationary with respect to the Therefore, when orbital speed of a satellite is increased by 2 earth. These satellites are used for communication times (41%), then it will escape from its orbit. purpose, and for weather forecasting, in studying the upper region of the atmosphere, in mapping etc. M The response of plants to gravity is called geotropism. Polar Satellites M Two types of effects are obtained in plants due to gravity. u The roots of plants always grow downward. — These satellites revolve around the earth in polar orbits u The stems (or shoots) of plants always grow upward. at a height of approximately 800 km. The time period of – Variation in the length of day time and night time from season to these satellites is approximately 84 min. season are due to revolution of the Earth on a tilled axis.  Self Check Build Your Confidence 1. Variations in the length of day time and night time from 2. Polar satellites are used for weather forecasting. season to season are due to [IAS 2013] Which of the statement(s) given above is/are correct? (a) the Earth’s rotation on its axis (a) Only 1 (b) Only 2 (b) the Earth’s revolution round the Sun in an elliptical manner (c) Both 1 and 2 (d) Neither 1 nor 2 (c) latitudinal position of the place (d) revolution of the Earth on a tilled axis 7. Consider the following statements. Statement I When a parachutist jumps from a height h 2. The known forces of nature can be divided into four metre, then graph relating displacement and time will be classes, viz, gravity, electromagnetism, weak nuclear parabolic. force and strong nuclear force. With reference to them, which one of the following statements is not correct? Statement II When a particle falling under gravity graph relating displacement and time will be straight line. (a) Gravity is the strongest of the four [IAS 2013] (b) Electromagnetism acts only on particles with an electric Which of the statement(s) given above is/are correct? charge (a) Only I (b) Only II (c) Weak nuclear force causes, radioactivity (c) Both I and II (d) Neither I nor II (d) Strong nuclear force holds protons and neutrons inside 8. Consider the following statements. the nucleus of an atom Statement I If a gymnast standing on a rotating stool 3. Ball bearings are used in bicycles, cars, etc, because with his arms stretched suddenly lowers his arms. His [IAS 2013] angular velocity increases. (a) the actual area of contact between the wheel and axle is increased Statement II A geostationary satellite is at an (b) the effective area of contact between the wheel and axle is approximate height of 10000 km. increased Which of the above statement(s) is/are correct? (c) the effective area of contact between the wheel and axle is (a) Only I (b) Only II reduced (c) Both I and II (d) Neither I nor II (d) None of the above 9. Consider the following statements. [IAS 2008] 4. Satellites used for telecommunication relay are kept in 1. A force is said to be conservative if the work done by the a geostationary orbit. A satellite is said to be in such an force on a particle in a round trip is zero. orbit when [IAS 2008] 2. A force is said to be non-conservative if work done by 1. the orbit is geosynchronous the force on a particle in a round trip is not zero. 2. the orbit is circular 3. The gravitational force and the electrostatic force are 3. the orbit lies in the place of the earth’s equator the examples of non-conservative forces. 4. the orbit is at an altitude of 22236 km 4. Viscous force and frictional force are the examples of Which of the statement(s) given above is/are correct? conservative forces. (a) 1, 2 and 3 (b) 1, 3 and 4 Which of the statement(s) given above is/are correct? (c) 2 and 4 (d) All of the above (a) 1, 2 and 3 (b) 1 and 2 5. Consider the following statements in respect of a jet (c) 3 and 4 engine and a rocket [IAS 2008] (d) 1, 2, 3 and 4 1. A jet engine uses the surrounding air for its oxygen supply and so is unsuitable for motion in space. 10. A metal ball and a rubber ball of the same mass are 2. A rocket carries its own supply of oxygen in the gas form dropped from the same height. After hitting the floor, the and fuel. rubber ball rises higher than the metal ball, why? Which of the statement(s) given above is/are correct? [IAS 2008] (a) Only 1 (b) Only 2 (a) Momentum is not conserved when the metallic ball hits (c) Both 1and 2 (d) Neither 1 nor 2 the floor 6. Consider the following statements. [IAS 2008] (b) The rubber ball hits the floor with greater velocity (c) Momentum i