General Science PDF in English

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Download All Subject Free PDF Child Development General Knowledge and Pedagogy Current Affairs History Maths Geography Reasoning Economics Science Polity Computer Environment General Hindi MP GK General English UP GK Join Our Best Course GK Trick By Nitin Gupta Current Affairs Daily Current Affairs PDF, Best Test Series, Best GK PDF के लिए हमें Follow करें Telegram Whatsapp हमें FOLLOW Instagram करें Apps Youtube  Head Office : B-32, Shivalik Main Road, Malviya Nagar, New Delhi-110017 Sales Office : B-48, Shivalik Main Road, Malviya Nagar, New Delhi-110017 Tel. : 011-26691021 / 26691713 INSTRUCTIONS Dear Student, Solutions to some of the selective problems are given separately in the form of e-book. The e- book is Additional Selective Solutions for General Science. You can access this book for Free by following some simple steps, (i) Visit www.educoreonline.com (ii) Click on Register and fill the required details to get registered. 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For further information about the books from DISHA, Log on to www.dishapublication.com or email to [email protected]  INDEX PHYSICS A-1-A-148 1. MEASUREMENTS1-9 Physical quantities, units ; Fundamental and derived units; Different system of units ; Prefixes for powers of 10, Errors in measurements, Significant figures; Some measuring devices ; Dimensions of Physical quantities. 2. MOTION 10-20 Rest and motion ; Distance, displacement, Position-time graph, speed, velocity and acceleration; Uniform and non-uniform motion, Uniformly accelerated motion; Velocity-time, position- time graphs; Equations of motion; Motion under gravity ; Relative velocity and Projectile motion. 3. FORCE AND LAWS OF MOTION21-31 Newton’s laws of motion ; Force and inertia, Momentum ; Impulse; Conservation of momentum, Forces; Friction ; Circular motion ; Banking of Road ; Centripetal and Centrifugal force. 4. WORK, ENERGY AND POWER32-38 Work ; Energy, Work-energy theorem ; Conservation of energy ; Transformation of energy; Power and Collisions. 5. CENTRE OF MASS AND ROTATIONAL MOTION39-47 Centre of mass; Rotational motion; Torque and couple, Angular momentum; Conservation of angular momentum ; Moment of inertia; Comparison of Rotational motion and Linear Motion. 6. FORCE OF GRAVITY48-56 The universal law of gravitation; Mass and Weight ; Acceleration due to gravity and its variation with altitude, depth and latitude; Kepler’s laws of planetary motion; Escape speed; Satellites; Free fall and Weightlessness. 7. SOLIDS AND FLUIDS57-67 Elasticity ; Stress and strain ; Hooke’s law; Modulus of elasticity; Fluid ; Density, Pressure in a fluid ; Atmospheric, Absolute and Gauge Pressure ; Pascal’s law, Archimedes' Principle. Viscosity, Stokes’ law; Terminal velocity; Streamline and turbulent flow; Bernoulli’s principle ; Surface tension; Angle of contact and capillary rise. 8. SOUND WAVES AND OSCILLATIONS68-79 Wave and its types ; Longitudinal and transverse waves; Characteristics of sound ; Reflection of sound ; Echo; Reverberation; Range of hearing ; Sonar ; Human Ear ; Interference of waves; Stationary longitudinal waves and air columns ; Beats ; Doppler effect in sound. Simple harmonic motion (S.H.M.) and its equation; Energy in S.H.M. - kinetic and potential energies; Simple pendulum ; Resonance. 9. HEAT AND THERMODYNAMICS80-90 Heat, temperature; Triple point of water ; Humidity ; Ideal-gas equation ; Thermal expansion; Specific heat capacity, Calorimetry; Change of state, latent heat; Heat transfer-conduction, convection and radiation; Thermal conductivity, Kirchhoff 's law, wein's displacement law; Newton’s law of cooling ; Thermodynamic processes ; zeroth law of thermodynamics ; First law of thermodynamics; Second law of thermodynamics: Reversible and irreversible processes; Heat engines; Refrigerators and heat pumps ; Carnot theorem. 10. ELECTRICITY AND MAGNETISM91-101 Electric charges: Basic properties of charge, Conductors and insulators, Cloud formation, Thundering and Lighting Coulomb’s law-forces between two point charges. Electric current : Ohm’s law, Electrical resistance, Electrical resistivity, Series and parallel combinations of resistors; Galvanometer, its current sensitivity and conversion to ammeter and voltmeter. Joule's law of heating, Household Circuits, safety Precautions. Magnetism : Permanent and Electromagnets, Magnetic effect of current, A.C. Generator or Dyanmo, DC motor, Transformer. Earth’s magnetic field and magnetic elements; Para-, dia- and ferro- magnetic substances; 11. LIGHT102-117 Light and its characteristics, Reflection of light ; Mirrors : Types, formula and magnification, Image formation by mirrors, Uses of concave and convex mirror; Refraction of light ; Refractive index ; Total internal reflection ; Lens : Types, formula, Image, formation by lens, power of lens, Interference, diffraction, polarisation of light, Human eye ; Defects of vision and their correction. Dispersion of light ; Rainbow, Scattering of light, Optical Instruments: Microscope, Telescope. Camera ; Primary and secondary colours of light. 12. MODERN PHYSICS118-129 Structure of the atomic nucleus ; Photoelectric effect, Einstein’s photoelectric equation. Mass- energy relation, mass defect; Binding energy per nucleon , Radioactivity-alpha, beta and gamma particles/rays and their properties; Radioactive Isotopes X-ray, Nuclear-reaction fission and fusion. Semiconductors; semiconductor diode: Diode as a rectifier;Junction transistor, Zener diode, photodiode and solar cell; Integrated Circuits. Communication :Basic elements of a communication system, modulation, demodulation; Propagation of electromagnetic waves; Sky and space wave propagation, Internet and Mobile Telephony. 13. SOURCES OF ENERGY130-138 Good Sources of Energy, Renewable, Non-Renewable and Conventional sources of energy; Thermal and Hydro power plants, Bio-Mass and Bio-Gas, Wind Energy. Non-conventional source of energy : Solar cell, Solar cooker, Energy from Sea : Tidal Energy, Ocean Energy, Nuclear Energy, Different Nuclear Power plants in India. 14. OUR UNIVERSE139-148 Origin of Universe : Big-Bang Theory, Galaxy, Stars : White Dwarf, Newtron stars, and Black Holes, Constellations, The Solar System : Planets, Asteroids, Comets, Meteors, Meteorites, Satellites, The Moon, Lunar and Solar Eclipses. CHEMISTRY B-1-B-154 1. CHEMISTRY AND ITS IMPORTANCE 1-11 Branches of Chemistry, The Importance and scope of Chemistry, Famous Chemists and their contribution Chemicals of Common Use 2. MATTER AND ITS COMPOSITION 12-20 Particulate Nature of Matter, Properties of Matter, Physical States of Matter, States of Matter, Effect of Temperature and Pressure on States of Matter 3. ELEMENT, MIXTURE AND COMPOUNDS 21-33 Elements, Compounds, Mixtures, Methods of Separation of the Components of Mixtures, Solution, Suspension and Colloid, Classification of Colloids, Physical and Chemical changes 4. ATOMS AND MOLECULES 34-44 Law of Chemical Combinations, Dalton’s Atomic Theory, Atoms, Atomic Symbols, Atomic Number, Mass Number and Isotopes, Atomic Mass, Molecule, ,Molecular Formula, Empirical Formula, Structural Formula, Molecular Mass, Equivalent Mass ,Ions, Avogadro's Law (Avogadro's theory; Avogadro's hypothesis), Avogadro’s Number and Molar mass of an element 5. ATOMIC STRUCTURE AND NUCLEAR CHEMISTRY 45-57 Fundamental particles of atom, Models of atom, Thomson Model, Rutherford’s Model, Bohr’s Model, Planck’s Quantum Theory, Modern Atomic Model, Quantum numbers, Arrangement of electrons in an atom, Nuclear Chemistry, Nature of Radiations, Nuclear Reactions, Rules for Writing a Nuclear Reaction, Artificial Radioactivity, Nuclear Fusion, Nuclear Fission, Application of Nuclear Fusion For The Benefit Of Mankind (Nuclear Reactor), Hydrogen Bomb, Uses of Radioactive Substances and Radiation 6. CLASSIFICATION OF ELEMENTS 58-65 Efforts for Classification, Dobereiner’s Triads, Newlands’ Law of Octaves ,Mendeleev’s Periodic Law and Periodic Table, Modern Periodic Law and Periodic Table, Classification of the elements, Trends in a Periodic Table 7. CHEMICAL BONDING AND REACTIONS 66-79 Lewis Dot Structure, Octet Rule, Types of Bonding, Ionic Bonding, Covalent Bond, Co-ordinate Covalent Bond, Exceptions to Octet Rule, Metallic Bonding,, Intermolecular Forces between Molecules, Chemical Reactions and chemical equations, Balancing Chemical Equations, Types of Chemical Reactions, Oxidation Number, Rules to Calculate Oxidation Numbers, Redox reaction in day-to-day life, Corrosion, Rancidity, Energy changes in Chemical Reactions. 8. THE CHEMISTRY OF ACIDS, BASES AND SALTS 80-91 Acids, Bases, concepts of Acids and bases , Arrhenius Concept , Bronsted–Lowry Concept, Conjugate Acid-Base pairs, Strength of Bronsted Acids and Bases, Lewis Concept of Acids and Bases,pH scale-the measure of acidity, Role of pH in Everyday Life, Buffer Solutions ,Types of Buffer Solution ,Salts, Classification of Salts ,Some Common Useful Salts 9. PROPERTIES, EXTRACTION AND USES OF METALS 92-104 Comparison of Metals and Non-Metals, Chemical Properties of metal, Reactivity Series, Extraction of metals-Metallurgy, Alloys, Some Important Metals and their uses. 10. NON-METALS 105-114 Properties of non-metals, Some important non-metallic elements, Hydrogen, Group 18 : Noble Gases, Group 17: Halogens,Group16: Chalcogens, Water (H2O),Group 15: Nitrogen, Group 14: Carbon, Glass, 11. INTRODUCTION TO ORGANIC CHEMISTRY 115-127 Differences between Organic and Inorganic Compounds, Catenation in Carbon, Functional Groups, Isomerism in Organic Compounds, Homologous series, Characteristics of Homologous Series, Hydrocarbons, Aliphatic Hydrocarbons, Aromatic Hydrocarbons, Alcohol (alkanol), Properties of Alcohols, Ethers, Properties of Ethers, Reactions of Ethers, Uses of Ethers, Amines, Properties of Amines, Reactions of Amines, Use of Amines, Alkanoic Acid (Carboxylic Acids),Properties of Carboxylic Acids, Reactions of Carboxylic Acids, Aldehyde (alkanols), Uses, Ketones (Alkanone), Esters , Reactions of Esters, Uses of Esters 12. CHEMISTRY AND MANKIND 128-144 Some important molecules of life , Carbohydrate, Amino Acids and Proteins, Peptides ,oil and fats, Hydrogenation of Oils ,Hormones ,Nucleic Acid ,Enzyme, Vitamins, Man-Made Molecules, Polymers Dye, Pigments, Paints, Drugs and Medicines, Fertilizers, Pesticides, Cement, Safety Matches, Ink, Gun-powder, Soaps and Detergents, Fuels 13. CHEMISTRY AND THE ENVIRONMENT 145-154 Damage to environment, Regional Environmental Damage, Global Environmental Damage, Pollution, Radioactive Pollution, Some Important Terms in Environmental Science BIOLOGY C-1-C-236 1. BIOLOGICAL CLASSIFICATION 1-16 Need for the biological classification-systemics, Binomial System, Five kingdom classification -Monera, Protista,Fungi, Plantae Animalia and Their Economic Importance. 2. CELL:FUNDAMENTAL UNIT OF LIFE 17-28 Cel theory, Cell structure-Cell Wall, cell membrane, Cytoplam-Endoplasmic reticulum, Golgi bodies, Lysosomes, vacuoles, Mitochondria, Plastids, Ribosomes, Centrosome and Centriole, Nucleus, Microbodies and Their funtions. 3. CELL CYCLE 29-40 Cell cycle:Phases of cell cycle:Interphase and M Phase, Amitosis, Mitosis and Meiosis. 4. TISSUE 41-57 Plant Tissue-Meristmetic Tissue, Permanent Tissue, Types and Their Functions ,Tissue system- Stomata, Vascular Bundle, Animal Tissue-Epithelial Tissue, Connective Tissue, Muscular Tissue, Nervous Tissue and Types and Their Functions. 5. NUTRITION 58-74 Nutrition in Plants: Types of Nutrition, Nutrients- Its Role, Function and Their Deficiency Symptoms, Photosynthesis, Nutrition in Animals : Their types, Nutrients : Its Role, Function and Their Deficiency Symptoms. 6. MORPHOLOGY AND PHYSIOLOGY OF PLANTS 75-94 Flowering Plants:Root,Stem, Leaf, Flower and their Characteristics, Functions and Its Economic Importance, Inflorescence, Discription of Some Important Families, Respiration In Plants, Respiratory Quotient, Transport In plants, Plants Growth and Development and Plant Diseases. 7. REPRODUCTION 95-113 Reproduction In Plants:Asexual Reproduction -Agamospermy, Spore Formation and Vegetative Propagation, Sexual Reproduction-Pre Fertilization, Fertilization and Post Fertilization, Fruit, Animal Reproduction:Asexual Reproduction-Fission, Budding and Fragmentation, Sexual Reproduction-Male and Female Reproductive System, Gametogenesis, Mentrual Cycle, Fertilization and Implantation, Parturition and Lactation, Reproductive Health- Methods of Birth Control, Sexually Transmitted Diseases and Infertility. 8. PHYSIOLOGY IN HUMANS 114-140 Digestive System In Humans: Alimentary Canal, Digestive Glands, Nutritional and Digestive Disorders, Respiratory System, Circulatory System, Excretory System, Control and Co-ordination-Nervous System, Chemical Control and Coordination, Skeletal System and Their Functions and Related Disorders. 9. HEALTH AND DISEASE 141-157 Diseases: Congenital, Aquired-Communicable and Non Communicable Diseases, Their causes Symptoms, Immune System-Their Cells and its Functions, Aids-Investigation, Treatment, Drugs and Alcohol Abuse. 10. EVOLUTION 158-171 Origin of Life:Theories, Spontaneous Generation, Millers and Ureys Experiment, Chemical and organic Evolution, Evidences of Organic Evolution, Theories, Geological Time Scale, Human Evolution. 11. GENETICS 172-184 Mendels Finding, Exceptions of Conclusion of Mendel, Linkage, Genes, Multiple Allele, Sex Determination, Genetic Disorders, Central Dogma of Molecular Biology and Human Genome Project. 12. BIOTECHNOLOGY 185-200 Principles and Processes, Recombinant DNA Technology, Application of Biotechnology, Hazards Arising Directly from The Inserted Gene, Biopiracy. 13. ECOLOGY AND BIODIVERSITY 201-218 Ecosystem:Structure and Function of Ecosystem, Food Chain, Food Web, Ecological Pyramid, Ecological Succession, Nutrient Cycling. 14. FOOD PROUCTION 219-236 Agriculture, Improvement in Crop Production, Irrigation system, Animal Husbandry, Apiculture, Fishries. SCIECNE AND TECHNOLOGY D-1-D-88 1. COMPUTER & TECHNOLOGY 1-24 History of Computer; Types of Computer; Components of a Computer; Computer Hardware; Information Technology; Storage Devices; Computer Technology; Pervasive computing; Computer Software; Basic of programming languages; Computer Network; Internet; Internet Governance; Security Issue in IT; Computer Viruses; Cybercrime; Development of it field; IT Industry in India; It and Government in India 2. COMMUNICATION 25-36 Recent communication technology; Modern telecommunication system; Information communication technology application; Near field communication Technology; Wire Communication; Networking Devices ; Nanotechnology in telecommunication; Wireless Communications; The Radio-Frequncy Spectrum; Telecom Spectrum; The Cellular Phone Technology ; MOBILE NETWORK; Generation of internet Technology: Telecommunication; History of Innovations in Telecommunication; Telecommunication In India; Digital television; Cable Television 3. DEFENCE 37-50 Location of Defence Establishments; Defence Production Undertakings; Nodal Agencies of Defence Sector; India’s Internal Security; India’s missile system; Nuclear-powered submarines; Aircraft carriers; Barak-Anti Missile; Shaurya Missile; DHRUV; IndARC; Indian Aircraft Carrier; Some Latest Aircrafts; List of Active Indian Military Aircraft; 4. SPACE TECHNOLOGY 51-63 Application of space technology; A geosynchronous orbit; Jet engine; Spacecraft; NASA's Deep Impact spacecraft SELENE-1; Bhuvan; Themis-Mission; Galileo is Europe’s Global Satellite Navigation System; Space Centres and Units; Indian Space Programme; INSAT System; Remote Sensing; Indian Remote Sensing (IRS) Satellite System; Launch Vehicle Technology; Cryogenic Engine; Export Promotion; Space mission 5. ENERGY 64-81 Energy; Feature of Energy; Source of Energy; Natural source; Application of energy; Energy Conservation; Energy Efficiency; Importance’s of Energy in Economic Development; Availability of Power in India; Energy Scenario in India; Fossil Or Conventional Energy Sources; Oil Shale; Electric Power; Electricity Generation in India Basic Power Generations Concept; Type of Power Station; Power Generating Capacity of India; National Rural Electrification Policy; Non-Conventional Sources of Energy; Contribution of non-conventional sources of energy for development of India; Waste Factors Responsible for Energy Potential. 6. NUCLEAR 82-88 Applications of Nuclear Energy; Nuclear reactors; Types of Nuclear Reactors; Nuclear Power  PHYSICS Chapter 1 MEASUREMENTS INTRODUCTION For example, velocity is derived from the fundamental quantities length and time, hence it is a The process of comparing an unknown physical derived physical quantity. quantity with respect to a known quantity is known as measurement. When we say that the length of our UNITS bedroom is 10 feet it implies that the bedroom is 10 times the known quantity ‘foot’ (feet is the plural To measure a physical quantity it is compared with a of foot). So, measurement of any physical quantity standard quantity. This standard quantity is called the consists of two parts – (i) a numerical value and (ii) unit of that quantity. the known quantity. The known quantity is called the For example, to measure the length of a desk, it unit of that physical quantity. is compared with the standard quantity known as Measurement is an integral part of physics. ‘metre’. Thus, ‘metre’ is said to be the unit of length. Physics is the foundation on which engineering, technology and other sciences are based. Handy Facts The unit named to commemorate a scientist is not written with capital initial letter. For example, PHYSICAL QUANTITIES the unit of force is written as newton (and not as Quantities which can be measured are called Newton), the unit of current is written as ampere physical quantities. Velocity, acceleration, force, (and not as Ampere) etc. area, volume, pressure, etc. are some examples of The symbols for units named after scientists physical quantities. are usually the first initial letter of their names in capital. For example, N for newton, A for ampere, Kinds of Physical Quantities J for joule etc. There are two kinds of physical quantities Types of Units Fundamental physical quantities: Fundamental There are two types of units : physical quantities are those which do not depend on other quantities and also independent of each Fundamental units: Fundamental units are those other. They are seven in number viz; length, mass, units which cannot be derived from any other time, thermodynamic temperature, electric current, unit, and they cannot be resolved into any basic or luminous intensity and amount of substance. fundamental unit. Also, the units of fundamental physical quantities are called fundamental units. Derived physical quantities: Derived physical The following table shows the seven fundamental quantities are those which are derived from fundamental physical quantities. units of S.I. System. A-2 Physics S. Fundamental Fundamental Symbol An international organization, the Conference No. Physical quantity Unit Generale des Poids et Mesures, or CGPM is internationally recognized as the authority 1. Length metre m on the definition of units. In english, this body 2. Mass kilogram kg is known as “General Conference on Weights 3. Time second s and Measure”. The Systeme International 4. Electric current ampere A de Unites, or SI system of units, was set up in 5. Temperature kelvin K 1960 by the CGPM. 6. Luminous intensity candela cd 7. Amount of mole mol Characteristics of a Standard Unit substance A standard unit must have following features to be accepted world wide. It should Derived units: Any unit which can be obtained by have a convenient size. the combination of one or more fundamental units are be very well defined. called derived unit. be independent of time and place. Examples: Area, speed, density, volume, momentum, be easily available so that all laboratories can acceleration, force etc. duplicate and use it as per requirement. Derived units of some physical quantities are as be independent of physical conditions like follows: temperature, pressure, humidity etc. S. Derived Physical Derived Unit be easily reproducible. No. quantity be universally accepted. 1. Area m2 Supplementary Units of SI System 2. Volume m3 3. Density kg/ m3 The following table shows the two supplementary 4. Speed m/s units of SI. System. 5. Acceleration m/s2 S.No. Physical Supplementary Symbol 6. Momentum kg m/ s quantity Unit 7. Force kg m/s2 or newton 8. Work kg m2/s2 or joule 1. Plane angle radian rad 9. Power kg m2/s3 or watt 2. Solid angle steradian sr 10. Charge ampere-sec or coulomb 1. radian (rad): The radian is the plane angle 11. Potential joule/coulomb or volt between two radii of a circle that cut off on the 12. Resistance volt/ampere or ohm circumference an arc equal in length to the radius. 2. steradian (sr): The steradian is the solid angle Systems of Units that, having its vertex at the center of a sphere, Depending upon the units of fundamental physical cuts off an area of the surface of the sphere equal quantities, there are four main systems of units, to that of a square with sides of length equal to namely the radius of the sphere. CGS (Centimeter, Gramme or Gram, Second) FPS (Foot, Pound, Second) Practical Units of Length MKS (Meter, Kilogram, Second) Astronomical unit, AU: The average distance SI (Systeme Internationale d′ Unites) between the sun and the earth about 1.49 × 1011 m is The first three of these systems recognize called 1 AU. only three fundamental quantities i.e. length Parsec: The parsec is defined to be the distance at (L), mass (M) and time (T) while the last one which a star would have a parallax angle equal to one recognizes seven fundamental quantities. i.e. second of arc. length (L), mass (M), time (T), electric current (I or A), thermodynamic temperature (K or q), 1 Parsec = 3.08568025 × 1016 m. amount of substance (mol) and luminous Light year : The light year is the distance travelled intensity (Iv). by light in one year. All electromagnetic waves travel Measurements A-3 at a speed of 299,792,458 ms-1 and an average year measure small lengths such as the wavelengths of being 365.25 days. light, atoms and molecules. One light year is 299,792,458 × 108ms–1 × (365.25 × 24 One angstrom ,1 Å =10–10m. × 60 × 60) s = 9.46073 × 1015 m. or 9.46073 × 1012 km. Fermi: A unit of length used to measure nuclear Angstrom: An angstrom is a unit of length used to distance = 10–15 meter, 1 fermi = 10–15m. PREFIXES FOR SI UNITS In Physics we have to deal from very small (micro) to very large (macro) magnitudes. To express such large and small magnitudes simultaneously we use following prefixes: Prefixes for powers of ten: Multiple of 10 Prefix Symbol Sub -multiple Prefix Symbol 1024 yotta Y 10–1 deci d 1021 zetta Z 10–2 centi c 1018 exa E 10–3 milli m 1015 peta P 10–6 micro µ 1012 tera T 10–9 nano n 109 giga G 10–12 pico p 106 mega M 10–15 femto f 103 kilo k 10–18 atto a 102 hecto h 10–21 zepto z 10 deca da 10–24 yocto y When a prefix is placed before the symbol of unit, the combined prefix and symbol should be considered as one new symbol which can be raised to a positive or negative power without any bracket, e.g., km3 means (103 m)3 but never 103 m3. ERRORS IN MEASUREMENTS (a) Instrumental errors: This type of error arises due to imperfect design or calibration of Generally measured value of a quantity is different the measuring instrument. For example from the true value of the physical quantity. The zero mark of vernier scale may not difference between the true value and measured value coincide with zero mark of main scale in a is called error. Error = true value – measured value vernier callipers. Before we discuss about errors let us understand two (b) Imperfection in experimental procedure: important terms : For example, measuring temperature of Accuracy : It is the measure of how close the measured a human body by placing thermometer value is to the true value of the physical quantity. under armpit would give lower Precision : It tells us about the limit or resolution upto temperature than the actual body which the quantity is measured. temperature, ignoring force of buoyancy during the measurement of weight of a Types of Errors body etc. Systematic errors : Those errors which tend to be in (c) Personal error: This type of error arise due one direction, either positive or negative, generally to lack of proper setting of the apparatus, their cause is known. These errors can be minimised individual bias, or due to carelessness by improving experimental techniques, selecting while taking observation. For example, if better equipment and removing personal bias. Some you hold your head towards right while of the sources of systematic errors are: reading ammeter or voltmeter there will be some error due to parallax. A-4 Physics (d) Errors due to external factors like variation in temperature, humidity, pressure, wind ∆a = × 100 etc. may introduce errors. For example amean wind may introduce error while taking the Final measurement in terms of the percentage error time period of a simple pendulum. will be expressed as (amean ± δa %). Random errors: These arise due to unpredictable and random variations in experimental conditions Science in Action like temperature, voltage supply, personal error by In sports, keeping accurate measurement of observer etc. These errors are also called ‘chance’ time is very important. In a 100 m race, even errors as these occurs irregular and are random time duration of 0.01 second become very with respect to sign (negative or positive) and size. important. A sports person can lose his/ her Random errors can be minimised by taking the observation several times and taking the arithmetic medal by a small fraction of time. mean of all the observations. Reliable and accurate system of units or Least count errors : The error associated with the measurements require for the fabrication of resolution of an instrument is called least count error. new instruments and machines that is the By using instrument of high precision and improving requirement for the commerce and trade experimental technique we can minimise least count worldwide. errors. Gross errors : These arise entirely due Significant Figures to carelessness of the observer like reading an Significant digits or figures give information about instrument without proper setting, recording the accuracy of a measurement. It tells us about observation incorrectly etc. This type of errors can the number of digits in which we have confidence. be minimised if the observer is mentally alert and Suppose a particular measurement is reported to be sincere. 9.28 cm, then the two digits 9 and 2 are reliable and Absolute, Mean Absolute, Relative and certain while the digit 8 is uncertain. The reliable Percentage Error and first uncertain digits are known as significant digits or figures. Absolute error : The magnitude of the difference There are certain rules for counting significant between the true value and the individual measured digits or figure: value is called absolute error of the measurement. Rule-1. All the non-zero digits are significant—For Absolute error An = amean – an example 2134 has four significant figures and 27184 It can be negative or positive or zero also. has five significant figures. Mean absolute error: It is the arithmetic mean of Rule-2. All the zeros between two non-zero digits magnitudes of absolute errors in all measurements. are significant, no matter where the decimal point i.e., Mean absolute error, is, if at all. For example 25089 has five significant figures, 12.0021 has six significant figures. ∆a + ∆a2 +....... + ∆an ∆a =∆amean = 1 Rule-3. In a number which is less than one all zeros n to the right of decimal point but to the left of a Relative or fractional error: It is the ratio of mean absolute error to the mean (true) value of measured non-zero digit are not significant. quantity. Rule-4. All the zeros on the right of last non-zero digits are significant in a number with a mean absolute error ∆a Relative error = = decimal point. For example in 3.500 there are four mean or true value amean significant digits and in 0.079000 there are five It is unitless significant figures. Percentage error : If relative error is expressed in Rule-5. All the zeros on the right on a non-zero terms of percentage then it is called percentage error digit are not significant in a number without decimal (da). point. For example 15800 has only three significant Percentage error (da) = relative error × 100 figures, 18930000 has only four significant figures. Measurements A-5 Rule-6. All the zeros on the right on a non-zero Uses of a Screw Gauge digit are taken to be significant when these come It is used to measure the diameter of a wire, thickness from a measurement. For example some distance of a thin metal sheet, etc. is measured to be 7890 m then this number would have four significant figures. Least Count (L.C.) Rule-7. A change of system of units does not The smallest division on the scale of the measuring change the number of significant digits in a instrument. It is an uncertainty associated with the measurement. Also when a number is written in scientific notation (a × 10b) then the powers of 10 resolution of the measuring instrument. are irrelevant to the determination of significant DIMENSIONS OF A PHYSICAL figures. QUANTITY SOME MEASURING DEVICES All physical quantities can be expressed in terms of These are instruments used for measuring a physical the fundamental quantities. Consider the physical quantity. Examples: vernier calliper, screw gauge, etc. quantity force. Vernier Calliper velocity Force = mass × acceleration = mass × Vernier calliper is a precision device which can time be used to measure internal and external distances length / time = mass × = mass × length × time–2 accurately. A vernier calliper is used for lengths to an time accuracy of 10–4 m. ∴ Unit of force = unit of mass × unit of length × Parts of Vernier Calliper (unit of time)–2 The main parts of vernier calliper are main scale, Thus we can express the unit of force as products of vernier scale, screw, jaws and strip. different powers of the fundamental units of mass, Uses of a Vernier Calliper length and time. It is used to measure length of a rod, diameter of a i.e., Force = [MLT–2] sphere, external and internal diameter of a hollow Thus the dimensions of a physical quantity are the cylinder, etc. powers to which the fundamental quantities mass, Screw Gauge length and time must be raised to represent it. An expression for a physical quantity in terms of Screw gauge is a device which is used to measure fundamental quantities is known as dimensional very small lengths or thickness up to one hundredth formula. part of a millimeter. A screw gauge is used to measure lengths as less as While writing dimensional formula we use symbols, to 10–5 m. M for mass, L for length, T for time, A for current, K for temperature, mol for amount of substance and cd for luminous intensity. Handy Facts A physical quantity may be dimensionless but still may have units. For example, plane angle is dimensionless but has radian as its unit. Parts of Screw Gauge The main parts of screw gauge are frame, main scale, A physical quantity that does not have any unit trimble, circular scale and ratchet. must be dimensionless. A-6 Physics Some Important Conversions (i) 1 yard = 0.9144 m ≅ 0.91 m (ii) 1 foot (1´) = 0.305 m (iii) 1 inch (1″) = 2.54 cm = 0.025 m (iv) 1 mile = 1609 m = 1.609 km (v) 1 l = 1000 cc = 10–3 m3 (vi) 1 mm = 10–3 m vii) 1 Chandra Shekher Limit (1 CSL) = 1.4 times the mass of the Sun (viii) 1 atomic mass unit 1 (amu) = 1.67 × 10–27 kg (ix) 1 slug = 14.57 kg, 1 pound = 0.4536 kg (x) 1 tonne = 10 quintal = 1000 kg (xi) 1 kg/m3 = 1000 g/cm3 18 (xii) 1 km/h = 5 m/s and 1 m/s = 18 5 km/h (xiii) 1 newton = 105 dyne, 1 kg wt = 9.8 N and 1 g wt = 981 dyne (xiv) 1 joule = 107 erg, 1eV = 1.6 × 10–19 J N dy (xv) 1 atm = 76 cm of Hg = 1.01 × 105 m = 1.01 × 106 cm 2 (xvi) 1 h.p. = 746 watt (xvii) 1 kw h = 3.6 × 106 J (xviii) 1 tesla = 1 web/m2 = 104 gauss (xix) 1 curie = 3.7 × 1010 disintegration/sec (xx) 1 rutherford = 106 disintegration/sec (xxi) 1 weber = 108 maxwell π 180 (xxii) 1 degree (1°) = radian and 1 radian = degree 180 π (xxiii) 1 shake = 10–8 sec Science in Action A spring balance on the moon will give different reading from that on Earth but a beam balance will give the same reading as spring balance requires gravity to measure. Mass remains same throughout but weight changes with gravity. Mass will only change if there is any change in the volume of matter in the body. Measurements A-7 EXERCISE 1. Which of the following systems of units is not 13. One micron equals to based on units of mass, length and time alone? (a) 10–3 m (b) 10–9 m (a) SI (b) MKS (c) 10 m–6 (d) 10–2 m (b) CGS (d) FPS 14. In SI units, candela is the unit of 2. Which of the following is not a unit of time? (a) current (b) temperature (a) Solar year (b) Tropical year (c) luminous intensity(d) none of the above (c) Leap year (d) Light year 3. Mass is the measure of 15. Practical unit of heat is (a) matter contained (b) weight (a) Calorie (b) Horse power (c) force (d) none of these (c) Joule (d) Watt 4. The mass is measured by 16. A complete turn means (a) a beam balance (b) a spring balance (a) p rad (b) p/4 rad (c) micro balance (d) none of these (c) 2 p rad (d) None of these 5. A hydrometer is used to measure – 17. Match List I (Units) with List II (Physical (a) density (b) mass quantity) and select the correct answer using (c) weight (d) R.D. the codes given below the lists. [CDS 2013] 6. Among the following the derived quantity is (a) mass (b) length List I (Units) List II (c) density (d) time (Physical quantity) 7. The SI unit of current is (A) Watt 1. Electric charge (a) kelvin (b) ampere (B) Tesla 2. Power (c) newton (d) volt (C) Coulomb 3. Luminous intensity 8. Which of the following is not a fundamental (D) Candela 4 Magnetic field unit? Codes (a) newton (b) kilogram A B C D (c) metre (d) second (a) 1 4 1 3 9. In SI units the number of basic physical (b) 1 2 3 4 quantities are (a) 3 (b) 7 (c) 1 2 4 3 (c) 9 (d) 21 (d) 2 4 3 1 10. The number of significant figures in 0.00060 m 18. Assertion : Number of significant figures in is 0.005 is one and that in 0.500 is three. (a) 1 (b) 2 Reason : This is because zeros are not (c) 3 (d) 4 significant. 11. Light year is [SSC CGL 2007] (a) If both Assertion and Reason are correct (a) light emitted by the sun in one year and Reason is the correct explanation of (b) time taken by light to travel from sun to Assertion. earth (c) the distance travelled by light in free space (b) If both Assertion and Reason are correct, in one year but Reason is not the correct explanation (d) time taken by earth to go once around the of Assertion. sun (c) If Assertion is correct but Reason is 12. The SI unit of pressure is incorrect. (a) atmosphere (b) bar (d) If Assertion is incorrect but Reason is (c) pascal (d) mm of Hg correct. A-8 Physics 19. Match List I (Physical quantity) with List II 26. Which one of the following is not a dimension (Units) and select the correct answer using the less quantity? codes given below the lists. (a) Strain (b) Relative density List I (Physical quantity) List II (Units) (c) Frequency (d) Angle A. Power 1. kg ms–1 27. Match list I (Product) with List II (Physical B. Energy 2. kg m2s–1 quantity) and select the correct answer using C. Momentum 3. Nm–2 the codes given below the lists D. Pressure 4. kW List I List II 5. kWh Codes (Product) (Physical quantity) A B C D A. Mass × velocity 1. Work (a) 4 5 1 3 B. Force × displacement 2. Power (b) 4 5 1 2 C. Force × perpendicular 3. Momentum (c) 5 4 1 2 distance of line of action (d) 5 4 2 3 of force 20. What is the correct sequence in which the lengths D. Force × velocity 4. Torque of the following units increase? Codes 1. Angstrom 2. Micron 3. Nanometer A B C. D Select the correct answer using the code given (a) 1 3 4 2 below: [NDA 2008-II] (b) 3 1 4 2 (a) 1, 2, 3 (b) 3, 1, 2 (c) 3 1 2 4 (c) 1, 3, 2 (d) 2, 3, 1 (d) 1 3 2 4 21. Multiply 107.88 by 0.610 and express the result 28. Match List 'I' (Physical quantity) with list II with correct number of significant figures (a) 65.8068 (b) 65.807 (Dimension) and select the correct answer by (c) 65.81 (d) 65.8 using the codes given below the lists. 22. Dimension of electromotive force are List I (Physical quantity) List II (Dimension) (a) [MLQ] (b) [ML2T–2] A. Density 1. [MLT–2] (c) [ML2Q–2] (d) [ML2T–2Q–1] B. Force 2. [ML–3] 23. The dimension of coefficient of viscosity is C. Energy 3. [MLT–1] (a) [MLT–1] (b) [ML–1T] D. Momentum 4. [ML2T–2] –1 (c) [ML T ] –1 (d) [ML–1] Codes 24. Assertion : Light year and wavelength both A B C. D measure distance. (a) 3 2 4 1 Reason : Both have dimensions of time. (b) 1 2 3 4 (a) If both Assertion and Reason are correct (c) 2 1 4 3 and Reason is the correct explanation of (d) 3 2 1 4 Assertion. (b) If both Assertion and Reason are correct, 29. The dimension [MLT–2] corresponds to but Reason is not the correct explanation [SSC CGL 2013] of Assertion. (a) force (b) work done (c) If Assertion is correct but Reason is (c) acceleration (d) velocity incorrect. 30. 'Farad' is the unit of [SSC CGL 2013] (d) If Assertion is incorrect but Reason is (a) resistance (b) conductance correct. (c) capacitance (d) inductance 25. [ML2T–2] are dimensions of 31. The dimension of strain is (a) force (b) moment of force (a) [M0L0T0] (b) [ML–1T] (c) momentum (d) power 2 (c) [M L T] 2 (d) None of these Measurements A-9 32. Assertion : Radian is the unit of distance. 38. Which one of the following pairs does not have Reason : One radian is the angle subtended at the same dimension? [NDA 2010-I] the centre of a circle by an arc equal in length (a) Potential energy and kinetic energy to the radius of the circle. (b) Density and specific gravity (a) If both Assertion and Reason are correct (c) Focal length and height and Reason is the correct explanation of Assertion. (d) Gravitational force and frictional force (b) If both Assertion and Reason are correct, 39. Match List I (Items) with List II (Unit of length) but Reason is not the correct explanation and select the correct answer by using the codes of Assertion. given below the lists. (c) If Assertion is correct but Reason is incorrect. List I (Items) List II (Units of (d) If Assertion is incorrect but Reason is length) correct. A. Distance 1 Microns 33. Which one is dimensionless? between earth (a) Force/acceleration and stars (b) Velocity/acceleration (c) Volume/area B. Interatomic 2 Angstroms (d) Energy/work distances in a 34. S.I. unit of surface tension is solid (a) degree/cm (b) N/m (c) N/m2 (d) N m C. Size of the 3 Light years 35. Match List I (Physical quantity) with list II nucleus (Units) and select the correct answer by using D. Wavelength of 4 Fermi the codes given below the lists. infrared laser List I (Physical quantity) List II (Units) A. Solid angle 1. pascal 5 kilometres B. Impulse 2. steradian Codes C. Viscosity 3. Newton-second A B C D D. Pressure 4. Pascal-second (a) 5 4 2 1 Codes (b) 3 2 4 1 A B C. D (c) 5 2 4 3 (a) 2 4 3 1 (d) 3 4 1 2 (b) 2 3 4 1 40. Assertion : Density is a derived physical (c) 1 4 3 2 quantity. (d) 1 3 4 2 36. A vessel contains oil of density 0.8 g/cm3 over Reason : Density cannot be derived from the mercury of density 13.6 g/cm3. A homogeneous fundamental physical quantities. sphere floats with half of its volume immersed (a) If both Assertion and Reason are correct in mercury and the other half in oil. The density and Reason is the correct explanation of of the material of the sphere in CGS unit is Assertion. (a) 3.3 (b) 6.4 (b) If both Assertion and Reason are correct, (c) 7.2 (d) 12.8 but Reason is not the correct explanation 37. If the energy E of a photon is equal to hn, where of Assertion. v is the frequency and h is Plank's constant, then (c) If Assertion is correct but Reason is the dimensions of Planck's constant is incorrect. (a) [ML2T–3] (b) [M0L2T–1] (c) [ML2T–1] (d) [ML2T–2] (d) If Assertion is incorrect but Reason is correct. ANSWER KEY 1. (a) 2. (b) 3. (a) 4. (a) 5. (a) 6. (c) 7. (b) 8. (a) 9. (b) 10. (b) 11. (c) 12. (c) 13. (c) 14. (c) 15. (a) 16. (c) 17. (a) 18. (c) 19. (a) 20. (c) 21. (d) 22. (d) 23. (c) 24. (c) 25. (b) 26. (c) 27. (b) 28. (c) 29. (a) 30. (c) 31. (a) 32. (d) 33. (d) 34. (b) 35. (b) 36. (c) 37. (c) 38. (b) 39. (d) 40. (c)  Chapter 2 MOTION INTRODUCTION which the position of the object changes in three directions. In this case the object moves in a space. Motion is everywhere. It is fundamental to our For example – a bird flying in the sky. human existence. Like all animals, we rely on motion to get food and to survive dangers. Like DISTANCE AND DISPLACEMENT all living beings, we need motion to reproduce, to Motion is related to change of position. The length breathe and to digest. Also, motion keeps us warm. travelled in changing position may be expressed in From everyday experience we recognise that motion terms of distance, i.e., the actual path length between represents continuous change in the position of an object when compared to a non-moving object i.e., two points. refrence point. Distance is a scalar quantity, which has only a magnitude with no direction. REST AND MOTION The direct straight line pointing from the initial point Rest : An object is said to be at rest if it does not to the final point is called displacement (change in change its position with respect to its surroundings position). Displacement only measures the change with the passage of time. in position, not the details involved in the change in Motion : A body is said to be in motion if its position. position changes continuously with respect to the Displacement is a vector quantity, which has both surroundings (or with respect to an observer) with magnitude and direction. the passage of time. The displacement can be zero, even if the distance Rest and motion are relative terms. is not zero. For example when a body is thrown Types of Motion on the basis of Dimensions vertically upwards from a point on the ground, after sometime it returns back to the same point, then the One-Dimensional Motion: It is the motion in which displacement of the body is zero but the distance the position of the object changes only in one direction. travelled by the body is not zero, it is 2h if h is the In this case the object moves along a line. For maximum height attained by the body. example – motion of a train along a straight line, Similarly, if a body is moving in a circular or closed freely falling object under gravity, etc. path and reaches its original position after one Two-Dimensional Motion: It is the motion in which revolution, then the displacement in one revolution the position of the object changes in two directions. is zero, but the distance travelled is equal to the In this case the object moves on a plane. For circumference of the circular path = 2πr if r is the example – projectile motion. radius of the circular path. Three-Dimensional Motion: It is the motion in Motion A-11 is time interval (change in time). Handy Facts The actual distance travelled by an object in a given The average speed of Cheetah is 70 m/s for 30 time interval can be equal to or greater than the seconds magnitude of displacement. It can never be less than Instantaneous Speed the magnitude of displacement. It is the speed at a particular time instant (t is The displacement of an object in a given time infinitesimal small or close to zero). interval can be positive, zero or negative. However, dx Vinst = Lt distance covered by the object in a given time dt →0 dt interval is always positive. If a particle covers two consecutive equal UNIFORM AND NON-UNIFORM distances with speeds v1 and v2 then, MOTION 2v1v2 Average speed = Uniform Motion v1 + v2 If a particle covers three consecutive equal It is a motion in which a body moves in a straight distances with speeds v1, v2 and v3 then, line (rectilinear) and covers equal distances in 3v1v2 v3 equal intervals of time. Average speed = The path length of a body in a uniform rectilinear v1v2 + v2 v3 + v3v1 motion is equal to the magnitude of the displacement. If a particle has speed v1 for time t1 and speed Consequently, the path length(s) in the motion is v2 for time t2 then, equal to the magnitude of the velocity (v) multiplied by the time (t) i.e., s = vt. v1t1 + v2 t2 Average speed = Handy Facts t1 + t2 No force is required to keep an object in uniform Uniform and Non-uniform Speed motion. When an object has uniform motion along a straight line in a given direction, the magnitude A body is said to be moving with uniform speed if it covers equal distances in equal time intervals and of displacement is equal to actual distance covered. with non-uniform or variable speed if covers unequal Non-Uniform Motion distances in the same time intervals. If a body covers unequal distances in equal SPEED WITH DIRECTION (VELOCITY) intervals of time, it is said to be moving with a non- Average Velocity uniform motion. It is a motion in which the velocity varies with time. The change in the velocity of It is defined as the ratio of change in position or a body in non-uniform motion is characterized displacement to the time taken. by acceleration. Uniformly variable motion is a x2 − x1 ∆x =v v= av = motion with a constant acceleration. Uniformly t2 − t1 ∆t variable motion can be curvilinear like circular Here x1 and x2 are the positions of the particle at time motion. If a uniformly variable motion is rectilinear, t1 and t2 respectively. Also, Dx = x2 – x1 = change in i.e., the velocity v changes only in magnitude, it position and Dt = t2 – t1 = change in time. Its unit is is convenient to take the straight line in which a ms–1, cms–1 or km h–1. material point moves as one of the coordinate axes (say, the x-axis). Instantaneous Velocity THE RATE OF MOTION Velocity of a body at a particular instant or moment Average Speed of time is called instantaneous velocity. ∆x It is defined as the total distance travelled divided by Instantaneous velocity vinst = lim ∆t → 0 ∆t the time interval to travel that distance. dx d or vinst = Average speed Vav = ,d is distance travelled, and t dt t A-12 Physics The magnitude of instantaneous velocity at an instant GRAPHICAL REPRESENTATION OF would always be equal to the instantaneous speed at that instant. MOTION IN A STRAIGHT LINE The velocity of an object may be positive, zero or Displacement-Time Graphs negative, but the speed of an object can never be negative, either zero or positive. A graph showing the Displacement = average velocity × time interval displacement of the y C  cyclist from A to C: This x = vt graph shows us how, in Displacement(m) Average velocity = (final velocity + initial velocity)/ 2  v+u t seconds time, the cyclist s v= has moved from A to C. 2 t We know the gradient RATE OF CHANGE OF VELOCITY (slope) of a graph is [ACCELERATION] defined as the change in y Average Acceleration divided by the change in x, It is defined as the change in velocity divided by the ∆y A x time interval to make the change. i.e.,. Time(s) ∆x   ∆v v − v0 , where a is average acceleration, ∆s a= = In this graph the gradient of the graph is just and ∆t t − t0 ∆t this is just the expression for velocity. Dv is change in velocity, and Dt is time interval. Instantaneous Acceleration The slope of a displacement-time graph gives the It is the acceleration at particular instant, velocity. mathematically, The slope is the same all the way from A to C, so ∆v dv ainst. = lim = the cyclist’s velocity is constant over the entire ∆t→0 ∆t dt displacement he travels. Instantaneous acceleration is also referred to as Observe the following displacement-time graphs. ‘acceleration’, Positive acceleration : If the velocity of an object Displacement Displacement Displacement increases in the same direction, the object has a positive acceleration. Negative acceleration (Retardation) : If the velocity of a body decreases in the same direction, the body Time Time Time has a negative acceleration or it is said to be retarding (a) (b) (c) e.g, a train slows down. Graph (a) shows the object is stationary over a Handy Facts period of time. The gradient is zero, so the When velocity of a particle increases with object has zero velocity. time, it is said to be accelerated motion i.e. Graph (b) shows the object is moving at a constant both acceleration and velocity will be positive velocity. You can see that the displacement and speed (magnitude of velocity) would increase. is increasing as time goes on. The gradient, When both acceleration and velocity are however, stays constant so the velocity is negative, that would mean that the direction of constant. Here the gradient is positive, so motion is in the opposite direction but in this case the object is moving in the direction we also speed of particle would increase with time. have defined as positive. If acceleration and velocity are of opposite Graph (c) shows the object is moving at a constant signs, in that case speed of the particle acceleration. You can see that both the would decrease. Deceleration is equivalent displacement and the velocity (gradient to negative of acceleration. of the graph) increases with time. The Motion A-13 gradient is increasing with time, thus the Handy Facts velocity is increasing with time and the The v-t graph of an object having uniform motion is a object is accelerating. straight line parallel to time-axis. The area between v-t Handy Facts graph of an object and time-axis is numerically equal The x-t graph of an object having uniform motion to distance covered by it. is a straight line inclined to the time-axis. The Acceleration-Time Graphs slope of straight line x-t graph gives velocity of the Observe the following acceleration-time graphs. uniform motion of the object. Velocity-Time Graphs Acceleration Acceleration This is the velocity-time graph of a cyclist travelling from A to B at a constant acceleration, i.e. with steadily increasing velocity. The gradient of this  ∆s graph is just and this is just the expression for Time Time ∆t (a) (b) acceleration. Because the slope is the same at all points on this graph, the acceleration of the cyclist is constant. Graph (a) shows an object which is either stationary or travelling at a constant velocity. Either B Velocity (m/s) 10 B way, the acceleration is zero over time. Graph (b) shows an object moving at a constant Velocity (m/s) v acceleration. In this case the t acceleration is positive - remember that it can also be negative. A Time A Time (s) 5 EQUATIONS OF MOTION The slope of a velocity-time graph gives the acceleration. Kinematic equations can be used to describe the motion with constant acceleration. Observe the following velocity-time graphs. First equation (Equation for velocity-time relation) : Final velocity Velocity Velocity = initial velocity + acceleration × time interval or v = u + at Time Time Second equation (Equation for position- (a) (b) time relation) : Graph (a) shows the object is moving at a constant 1 velocity over a period of time. The Displacement = initial velocity × time interval + 2 gradient is zero, so the object is not × acceleration × time interval2 accelerating. 1 or s ut + at 2 = Graph (b) shows an object which is decelerating. 2 You can see that the velocity is decreasing Third equation (Equation for position- with time. The gradient, however, stays 2 velocity relation) : v= u 2 + 2as constant so the acceleration is constant. Here the gradient is negative, so the object Final velocity2 = initial velocity2 + is accelerating in the opposite direction to 2 × acceleration × displacement its motion, hence it is decelerating. or v2 = u2 + 2as A-14 Physics RELATIVE MOTION The value of acceleration due to gravity (g) is taken as The motion of an object B w.r.t. object A which is 9.8 m/s2, 980 cm/s2 or 32 ft/s2. moving or stationary is called as relative motion. Let us consider the three cases discussed below. Relative velocity of an object B w.r.t. object A Case-I: Body thrown downward : when both are in motion is the rate of change of In this case, initial motion of the body is downward u g position of object B w.r.t. object A. Relative velocity of object B w.r.t. object A, so according to the sign VBA = VB - VA convention, downward Relative velocity of object A w.r.t. object B, direction will be taken h as positive and upward VAB = VA - VB direction as negative. So, When both the objects A and B move in the same the kinematic equations direction will be : VAB = VA - VB (i) v = u + gt When the object B moves in the opposite direction v 1 2 of A (ii) h = ut + gt VAB = VA + VB 2 When VA and VB are inclined to each other at (iii) v2 = u2 + 2gh 1 angle q. (iv) hnth = h + g (2n – 1) 2 VAB = V A2 + V B2 + 2VA + VB cos (180° - θ) In a special case when the body is dropped/let falls i.e., initial velocity (u) = 0, then equation becomes = V A2 + V B2 - 2VA VB cos θ 1 1 v = gt ; h = gt2 ; v2 = 2gh ; hnth = g (2n – 1) If VAB makes angle q with VA, then 2 2 V sin q Science in Action tan q = V -BV cos q A B According to Galileo, when two bodies of different Above formulae are useful in finding Rain-man, masses are dropped from the same height both will River-Boat problems. touch the floor at the same time in the absence of Science in Action air resistance. If a ping pong and basket ball are The boat which sails directly with the wind dropped the floor from same height, they will hit cannot sail faster than the wind speed because at the same time in the absence of air resistance. sailing as fast as the wind, there would be no Case-II: Body thrown upward: wind impact against the sail, it would sag. If it If a body is thrown vertically up with an initial is sailing crosswinds, there would still be wind velocity (u). impact against the sail, but in this case speed of Hence a = – g. Kinematic equations will be: 1 boat is greater than wind speed can be achieved. (i) v = u – gt (ii) h= ut − gt 2 2 MOTION UNDER GRAVITY 2 2  1 (iii) v – u = – 2gh (iv) hn = u – g  n −   2 It is a common experience that when a body is dropped Maximum height reached by the body form a certain height it experiences acceleration From equation v2 = u2 + 2gh due to gravity and its motion is in a straight path. u2 Similarly, when a body is thrown vertically up, it H = [∵ v = 0] 2g goes to a certain height and then starts falling again, Therefore, the maximum height reached by the body experiencing acceleration due to gravity throughout is directly proportional to the square of the initial the motion. velocity. Motion A-15 Time of ascent (ta): The time taken by a body thrown from the top of building, a bomb released thrown up to reach maximum height ‘h’ is called its from a plane. time of ascent. Y u ta = g u B Hence time of ascent ta is directly proportional to the initial velocity u. Time of descent (td): The time taken by a freely uy H α u Maximum falling body to reach the ground is called the time x height A of descent. O X Horizontal range, R 2h td = The path followed by a projectile is called its trajectory, g mostly, the trajectory of a projectile is parabolic. a=+g v 2 v h gx 2 = and h = , td Equation of trajectory y = x tan α - 2g g 2u cos 2 x y = x tan α b1 - R l x u or v=u But, we know that u = v i.e., projected velocity of a Maximum height (H): When a projectile moves, it body is equal to the velocity of the body on reaching covers a maximum distance in vertical direction. This the ground. maximum distance is called the maximum height u attained by the projectile. ∴ td = = time of ascent (ta) 2 2 g Maximum height H = u sin α Time of ascent = time of descent 2g Horizontal range (R): The horizontal distance Velocity on reaching ground: When a body is between the point of projection and the point of dropped from a height h, its initial velocity is zero. landing of a projectile. v2 – u2 = 2gh but u = 0 2 Maximum range R = u sin 2α ∴ v2 – 0 = 2gh or, v = 2gh g Time of flight (T): The time taken by the projectile Case-III: Body projected vertically up from the to reach the point of landing from the point of top of a tower : projection. If a body is projected vertically up from the top of a Time of flight T = 2u sin α tower of height ‘h’ with velocity ‘u’. Then g 1 Science in Action Displacement after time t is = s ut − gt 2 An aeroplane flying at a constant speed, if 2 Velocity after time t is v = u – gt. it releases a bomb, the bomb moves away from the aeroplane and it will be always Velocity on reaching the ground is u 2 + 2 gh vertical below the aeroplane as the horizontal Maximum height above the ground is {h + (u2 /2g)} component of the velocity of the bomb will be same as that of the velocity of the aeroplane. PROJECTILE MOTION And thus the horizontal displacement remain Projectile is the name given to a body thrown with same at any instant of time. some initial velocity in any arbitrary direction If two bullets are fired horizontally, simultaneously and with different velocities and then allowed to move under the influence of a from the same place, both the bullets will constant acceleration. The motion of a projectile is hit the ground simultaneously as the initial called projectile motion. velocity in the vertically downward direction Example : A football kicked by the player, a stone is zero and same height has to be covered. A-16 Physics EXERCISE 1. The numerical ratio of displacement to the [NDA 2008 – II] distance covered is always. (a) Displacement (b) Kinetic energy (a) less than one (c) Acceleration (d) Velocity (b) equal to one 10. Which one of the following graphs represents (c) equal to or less than one motion? [CDS 2010 – II] (d) equal to or greater than one 2. If an object is in a state of equilibrium velocity velocity (a) it is at rest (a) (b) (b) it is in motion at constant velocity time (c) it is in free fall time displacement (d) may be more than one of the above displacement 3. The speed of a falling body increases continuously, this is because (c) (d) (a) no force acts on it (b) it is very light time time (c) the air exert the frictional force 11. A passenger in a moving train tosses a five (d) the earth attract it rupee coin. If the coin falls behind him, then 4. An iron ball and a wooden ball of same radius the train must be moving with a uniform are released from a height ‘h’ in vacuum. (a) acceleration (b) deceleration Which of the two balls would take more time (c) speed (d) velocity to reach the ground? 12. Which of the following distance-time graph (a) Iron ball (x-t) represents one-dimensional uniform (b) Both would take same time motion? [CSAT 2001 – I] (c) Wooden ball x x (d) None of these 5. When the brakes are applied on a moving cycle, the directions of velocity and acceleration are (a) (b) (a) opposite (b) same (c) perpendicular (d) not related 6. Slope of a velocity–time graph gives t t (a) the distance (b) the displacement (c) the acceleration (d) the speed x x 7. The numerical ratio of displacement to distance for a moving object is (a) always less than 1 (c) (d) (b) always equal to 1 (c) always more than 1 t t (d) equal or less than 1 8. If an object undergoes a uniform circular 13. A stone is thrown vertically upwards with an motion, then its [NDA 2013 – I] initial velocity u from the top of a tower of (a) acceleration remains uniform 12u2 (b) velocity changes height g. With what velocity does the (c) speed changes stone reach the ground ? [NDA 2006 – I] (d) velocity remains uniform (