gekjk fo"k;&izokg lgt ugha jgrk gsa vksj] fcuk lgt izokg ds u gh eu yx ldrk gs vksj u gh i<+us&i<+kus esa vkuun fey ldrk gsa

Transkript

1 Zero syllabus ifjp;& dksbz Hkh fo"k; i<+uk ;k i<+kuk vkjahk djus ds iwoz gesa mldh i`"bhkwfe ds lakku dk gksuk vr;ar vko';d gsa ;g lakku fo'ks"kdj fokku laca/kh fo"k;ksa ds fy;s T;knk egroiw.kz gs D;ksafd bu fo"k;ksa dh ikfjhkkf"kd 'kcnkoyh vu; lkekftd fo"k;ksa dh 'kcnkoyh ls dbz ekeyksa esa fhkuu gksrh gsa ;g crkus dh vko';drk ugha fd fdlh Hkh fo"k; dks le>us ;k mls izlrqr djus ds fy;s rduhdh vksj ikfjhkkf"kd 'kcnksa ls ifjfpr gq, cxsj vkxs c<+uk vksj fo"k; esa izokg dks cuk;s j[kuk dfbu gksrk gsa ifjfpr 'kcnksa ds lkfk tc dh izfdz;k vkjahk gksrh gs rc fo"k;&izos'k vklku gks tkrk gs o fo"k; esa Lor%,d izokg cu tkrk gsa ;g ifjfpr jklrs ij pyus tslk gksrk gsa tc le> ds Lrj ij lqyrk feyus yxrh gs rc f'k{kd@fo kfkhz vkuun ls jksekafpr gksus yxrs gsaa lp rks ;g gs fd fo"k; ds v/;;u@v/;kiu ds nksjku ifjfpr 'kcnksa ds feyus ls cksfj;r ugha gksrh] /;ku vklkuh ls cuk jgrk gs vksj eu ds HkVdus ij Lor% jksd yx tkrh gsa lkeku;r% fokku laca/kh fo"k;ksa esa HkkSfrdh ls fo kfkhz dqn vf/kd gh Hk;Hkhr jgrs gsaa tcfd ckr,slh gksuk ugha pkfg;sa HkkSfrdh rdz ij vk/kkfjr fo"k; gs ftlds v/;;u esa mu?kvukvksa dk lekos'k gksrk gs ftugsa ge vius vklikl?kvrs gq, ns[krs gsa] lqurs gsa vksj eglwl djrs gsaa HkkSfrdh; v/;;udrkz dk mn~ns'; ftkklk isnk djus okyh gj?kvuk dks le>uk vksj muds ihns fnis dkj.kksa dks tkuuk gksrk gsa,slk gksus ls izd`fr ds fu;eksa dk irk pyrk gsa HkkSfrdh; v/;;udrkz fqj mu fu;eksa dks vk/kkj eku dj vuqiz;ksx djuk pkgrk gs vksj vkxs fnih ubz lahkkoukvksa dks ryk'kuk pkgrk gsa og viokn Lo:i mu?kvukvksa dks Hkh tkuuk pkgrk gs tgk ;s fu;e dke u djrs gksaa bl rjg vc vxj ewy :i esa ns[ksa rks gesa vius vklikl inkfkz] ÅtkZ o vkdk'k fn[krs gsa vksj dky cgrs gq, izrhr gksrk gsa vr% HkkSfrdh gesa inkfkz vksj mldh xfr ls tqm+k fokku utj vkrk gsa inkfkz pkgs vkosf'kr gks ;k fujkosf'kr] lw{e gks ;k LFkwy & HkkSfrdh; n`f"v mls fof'k"v cuk nsrh gsa blhrjg xfr;k pkgs og LFkkukUrj.kh; gks ;k?kw.khz ;k nksyuh;] HkkSfrdh; n`f"v im+us ij os izd`fr ds jkt [kksyrs utj vkrh gsaa tsls tsls gekjs lkeus izd`fr ds jkt [kqyus yxrs gsa gesa vikj vkuun dh vuqhkwfr gksus yxrh gs ftlls HkkSfrdh esa gekjh :fp c<+us yxrh gsa ysfdu ;g fugk;r O;fDrxr ekeyk gsa vkjafhkd dfbukb;k rks vkrh gsa ysfdu bugsa ikj djrs gh etk vkus yxrk gsa HkkSfrdh; v/;;u esa gj?kvuk ij /;ku nsuk] ladsrksa dks xzg.k djuk] fo'ys"k.k djuk vksj varlzeca/kksa dks [kkst dj fdlh rdzleer fu"d"kz ij igq puk gksrk gsa blrjg HkkSfrdh; v/;;u inkfkz dh cká nqfu;k ls inkfkz dh vkarfjd nqfu;k esa izos'k dk jklrk lqyhk djkrk gsa ;g v/;;u i<+us&i<+kus okyksa dks ogk ys tkuk pkgrk gs tgk og ns[kk tk lds tks vk[kksa dh {kerk ls Hkh ijs gks] tgk og lquk tk lds tks dkuksa dh {kerk ls Hkh ijs gks vksj tgk og eglwl fd;k tk lds tks dkweu lsal ls Hkh ijs gksa blds fy;s HkkSfrdfon~ ekwmy dk lgkjk ysrs gsa] fl)kar x<+rs gsa vksj ifjdyiuk cukrs gsaa fqj os mugsa tk prs&ij[krs gsa vksj HkkSfrdh dk <+kpk [km+k djrs gsaa gj d{kk dk viuk ikb~;dze gksrk gsa mldk vk/kkj iwoz dh d{kkvksa esa i<+s x;s ikb~;dze gksrs gsaa fcuk vh;kl ds cht&'kcnksa vksj ikfjhkkf"kd o rduhdh&'kcnksa ds vfkz ;kn ugha jgrsa ;g i<+us&i<+kus esa ck/kk mriuu djrk gsa blhfy;s vko';d gs fd ge tc bugsa le>uk vkjahk djrs gsa rks LokHkkfod gh dqn dfbukb;k lkeus vkus yxrh gsaa blls cpus ds fy;s ;g vko';d gs fd i<+us&i<+kus ds iwoz ge mu cht&'kcnksa vksj rduhdh&'kcnksa dks tku ysa ftuls iwjs ifjp; ds fcuk 1

2 gekjk fo"k;&izokg lgt ugha jgrk gsa vksj] fcuk lgt izokg ds u gh eu yx ldrk gs vksj u gh i<+us&i<+kus esa vkuun fey ldrk gsa HkkSfrdh ds fy;s 'kwu; ikb~;øe dh jpuk& HkkSfrdh ds fy;s 'kwu; ikb~;øe dh jpuk djus ds ihns gekjh blh Hkkouk us dk;z fd;k gsa blesa mu cht&'kcnksa vksj ikfjhkkf"kd o rduhdh&'kcnksa ds lkfk gh xf.krh; rduhdksa dks lfeefyr fd;k x;k gs ftudh t:jr d{kk 11oha ds HkkSfrdh ds ikb~;dze dks i<+rs le; gksrh gsa ;g 'kwu; ikb~;dze yphyk gsa blesa cgqr dqn tksm+k vfkok?kvk;k tk ldrk gsa ;g iwjh rjg vki ij fuhkzj gsa vxj i<+krs le; vki eglwl djrs gsa fd cpps HkkSfrd jkf'k;ksa dh foek vksj bdkbz le>us esa Hkzfer gksrs gsa ;k dfbukbz eglwl djrs gsa rks 'kwu; ikb~;dze esa bugsa folrkfjr :i esa 'kkfey fd;k tk ldrk gsa ysfdu vxj os xf.krh; rduhdksa ds vuqiz;ksx ls?kcjkrs gsa rks 'kwu; ikb~;dze esa bu ij fo'ks"k /;ku fn;k tk ldrk gsa 'kwu; ikb~;dze dh le;kof/k fuf'pr ugha dh tk ldrh gsa ;g rc rd pyk;k tkuk pkfg;s tc rd fd cppksa ds dkulsiv~l vpns u gks tk;saa fcuk vpns dkulsiv~l ds HkkSfrdh i<+us dk mn~ns'; iwjk ugha gks ldrk gsa ;g f'k{kd ij fuhkzj djrk gs fd mls fdl fglls ij fdruk /;ku nsuk gsa bl ikb~;dze dk eq[; mn~ns'; gs fd fo kfkhz i<+rs le; fo"k; esa lgt izokg eglwl djsa vksj vius esa :fp isnk djrs gq, ftkklq curs pys tk;saa General terms Axiom ¼Lo;afl) dfku½: it is a mathematical statement which is assumed to be truth without proof falsify is yet to be established Conjecture¼vuqeku yxkuk½: it is a mathematical statement whose truth or falsify is yet to be established Hypothesis ¼ifjdYiuk½: proposition made as a basis for reasoning without the assumption of its truth. It is supposition made as a starting point for further investigation from known facts. It may be called groundless assumption. Law ¼fu;e½: a statement of fact to the effect that a particular phenomenon always occurs if certain conditions are present Proof ¼izek.k½: A process which can establish the truth of a statement based purely on logical arguments Theorem ¼izes;½: It is a mathematical statement whose truth has been logically established Meaning of the words that appear in questions Discuss: examine and argue about Describe: give a picture in words Elaborate: describe in detail with much care Write: put down by means of words Generalization: more common or more widely applicable Linearization: Able to be presented by a straight line on a graph 2

3 What is physics? Its origin is latin word physica. Its meaning is natural things. Physics deals with matter, energy, space and time. System Subsystem Environment Physical Parameters Parameters related to translatory and rotatory motions Adhesion: its meaning is sticking to surface. The adhesive force is the inter molecular attraction between unlike molecules. Atomic mass: sum of the neutron and protons Atomic number: number of protons Capacity: the inner volume of a container Central force: r-dependent forces are known as central forces. The gravitational, electrostatic and magnetic forces are examples of central forces. Centre of mass: the point at which the mass of the body may be considered to be concentrated. It is the point from which the sum of the moment of mass (product of the mass of element and its distance from the centre of mass) of all the elements of the body is zero. Cohesion: its meaning is holding together. The cohesive force holds a solid or liquid together due to inter molecular attraction. This force decreases with rise in temperature. Degrees of freedom: the number of independent ways in which a system may possess translational, vibrational and rotational motions. Density: In general, it is mass density called as only density and is defined as mass per unit volume. But for uniform surface, it may be surface mass density and is defined as mass per unit surface area. For a uniformly thin rod, it may be linear mass density and is defined as mass per unit length. It may be defined to express the density of charge. For charge it is called volume charge density and is defined as charge per unit volume. The surface and linear charge densities are defined accordingly. Different kind of forces: in general, we have two types of forces: contact and non-contact forces. The familiar forces are gravitational, mechanical, frictional, cohesive, adhesive, muscular, nuclear, electrostatic, magnetostatic, electromagnetic, nuclear etc. Distance and displacement: the distance is scalar quantity but the displacement is vector. If a particle moving on a circular path completes one round, then the displacement of the particle is zero but the distance covered by it is 2πr Elastic collision: it is the collision in which conservation of momentum and kinetic energy hold. In other words, for such collision, momentum and kinetic energy before collision are equal to the momentum and kinetic energy after collision. During inelastic collision, kinetic energy is not conserved. 3

4 Elasticity: the property of the body of resuming its original form and dimensions when the impressed forces upon it are removed. If the forces are sufficiently large for the deformation to cause break in the molecular structure, it loses its elasticity and the elastic limit is said to be reached. Hook s law (stress is proportional to strain) acts only within elastic limit. The behaviour opposite to that of elasticity is known as plasticity. No any material is 100% elastic or plastic. Energy: ability to do is called energy. Its unit is joule. It may have different forms. It may be light energy, or sound energy, electromagnetic energy, heat energy, magnetic energy, electrical energy, chemical energy, nuclear energy. In general the energy is classified as kinetic energy and potential energy. If we do some work on the body, it is stored as potential energy in the body. Potential energy is a measure of capacity of the body to do the work. The kinetic energy is possessed by the moving bodies. For translational motion it is equal to ½ mv 2 and for rotational motion it is ½ Iω 2. Equations of motion: v = u + at; s = ut +1/2 at 2 ; v 2 = u 2 + 2as. Equilibrium: A state of balance between opposing forces or effects Field: the region in which a massive body, electric charge, a magnetic body exerts its influence. A field is actually a model for representing the way in which a force can exist between bodies not in contact. Floatation, principle: (Archimedes principle) the weight of the liquid displaced by a floating body is equal to the weight of the body. If the weight of the floating body is more than the weight of the liquid displaced, the body sinks. Fluids: Gases and liquids together are called fluids. Force: It is a vector quantity. It is defined using Newton s second law of motion. According to this, the rate of change of momentum is called force. Or, it is the differential coefficient of momentum with respect to time. Its unit is Newton. Friction due to liquids and gases: Liquids exerts less force of friction and the gases the least as compared to solid. Friction: An opposing force that appears when two surfaces in contact with each other try to move relative to each other. Friction is a necessary evil. Without friction neither the bodies can be set in motion nor can the moving bodies be stopped. Use of lubricants, soap solutions, fine powders and polishing can reduce friction. Friction: It is the force that offers resistance to relative motion between surfaces of contact. The static coefficient of friction is the ratio of the frictional resistance when the body is about to slide along a specified surface (F s ) to the perpendicular force (R) between the surface in contact. The kinetic coefficient of friction is the ratio of the frictional resistance when the body is sliding steadily along a specified surface (F k ) to R. Fundamental forces of nature: Gravitational, electromagnetic, nuclear strong and nuclear weak forces. Graphs and extrapolation of the curve in the graph Impulse: It is the product of force and the duration during which it acts. Isotope: The elements having same atomic number but different atomic mass numbers. 4

5 Latitude: The angular distance of a point from the equator measured upon the curved surface of the earth. The latitude of equator is zero and that of poles are 90 o. Law of conservation of energy: Energy before event is equal to energy after event. This law is a direct consequence of third law of motion. Law of conservation of momentum: Momentum before event is equal to momentum after event. This law is a direct consequence of third law of motion. Laws of motion: There are three laws. First law: if a body continues to remain in the state of rest or uniform motion unless and until an external force acts on it; Second law: the rate of change of momentum is force; Third law: to every action there is an equal and opposite reaction. Lever: It is a bar that is free to move about the point (called fulcrum) on which it rests. The object to be moved is called load or resistance and the force applied is called effort. There are three classes of lever. Linear: Means arranged in a line. It has only one dimension. The system is known to be linear if the output is proportional to input. Longitude: The angle which the terrestrial meridian through the geographical poles and the point on the earth s surface makes with a standard meridian (passing through Greenwich). Machine: It is a devise which makes work easier to do. There are six simple kinds of machines viz. lever, inclined plane, wedge, screw, wheel-and-axel and pulley Manometer: It is a devise to measure the pressure. Meteors: Shooting stars Moment of force: It is called torque. It is a measure of the tendency of a force to rotate the body to which it is supplied. It is measured by multiplying the magnitude of the force by the perpendicular distance from the line of action of the force to the axis of rotation. Moment of inertia: It is the sum of the products of the mass dm of each element of the body (a body is assumed to be made of a large number of infinitesimal elements of mass dm) and square of its distance from the axis of rotation. Moment of momentum: It is angular momentum and is equal to product of moment of inertia and angular velocity Momentum: It is a vector quantity. it is the product of mass and velocity. Power: It is rate of doing work. Its unit is joule/second. it is also known as watt. Pressure: It is defined as force per unit area. Its unit is Newton/m 2 and is called pascal. The pressure increases with depth in the liquids. Deep sea divers have to wear specially designed suits, otherwise the huge pressure of water will crush their bodies. The dams are thickened at the base to withstand huge pressure. At high altitudes, air pressure is very small. Pull and Push: These are forces. Push or pull changes the speed and direction. In other words, they change velocity. Pulse: A brief increase in the magnitude of a quantity whose value is usually constant 5

6 Quantities that characterise motion: Displacement, velocity, momentum, acceleration, force, kinetic energy and potential energy Relative density: It is the ratio of density of substance to the density of water. Rolling friction: It is the friction experienced by the body when it is made to move over bodies like roller. It is far less than sliding or dynamic friction (about 10 times). The ball bearings (small steel balls) are introduced between the sliding surface of the axel and the cup. Speed and velocity: Speed is scalar quantity but velocity is vector. The speed is rate of change of distance covered but the velocity is the rate of change of displacement Speed: It is the rate of change of distance covered. Speed = distance/time. It is also defined as differential coefficient of distance with respect to time. States of matter: In general, there exists four states of matter, viz., solid, liquid, gas and plasma. This classification is based on general properties of matter. However, matter may be classified on the basis of other properties. On the basis of optical properties the states are: opaque, translucent and transparent. On the basis of electrical properties the states are: insulator, semiconductor, conductor and superconductor. The classification can also be made on the basis of thermal and magnetic properties. Stethoscope: It is a devise that amplifies the sound of a heart beat and other sounds in the chest and back. Stream line and turbulent flow: The type of fluid flow in which the motion at any point varies in magnitude and direction. The fluid flow in which this doesn t happen is called stream line flow. Thrust: The compressive force applied by the material. Uniform motion: When the speed remains constant, we call motion to be uniform. Nonuniform motion results if the speed is not uniform. m1m Universal law of gravitation: F = G 2 r 12 2 Velocity: It is the rate of change of displacement. Or, it is differential coefficient of displacement with respect to time. Viscous: Having high viscosity. Viscosity is the property of fluid whereby it tends to resist relative motion within itself. The fluid may be modelled as made of thin layers. If different layers of fluid are moving with different velocities, viscous forces come into play, tending to slow down the faster moving layer and to increase the velocity of slower moving layers. The viscous force is proportional to the velocity gradient between the layers. The constant of proportionality is called coefficient of viscosity. Weight of the body: F = mg Work: It is said to be done only if the force moves the object. It is a scalar quantity and is defined as a scalar or dot product of force and displacement. Parameters related to waves and oscillations Amplitude: It is the maximum displacement of vibrating body. Audible range of sound; 20 to herz. 6

7 Coupling: Connecting the two systems; coupled oscillators are two oscillators coupled by, say, a spring. Damped and undamped vibrations: Vibrations whose amplitude doesn t change with time are known as undamped vibrations. But if amplitude changes with time, they are damped vibrations. Damping: A decrease in the amplitude of an oscillation or wave motion with time. Doppler effect: The apparent change in frequency due to relative motion between source or listener. Echo: The reflection of sound from hills or big buildings is called echo. Frequency; it is the number of oscillations per second. n = 1/T Infrasound: The sound whose frequency is less than 20 hertz. It is not audible to human ears Intensity of sound: It depends upon amplitude. It also depends upon the inverse square distance from the source and area of the vibrating body. I A 2, I 1/d 2 and I S. the loudness depends upon the density of medium also. Lesser the density, lesser loud is the sound. Longitudinal: Lengthwise. In a line with the length of the object. Longitudinal vibration of a body is that in which the line of oscillation coincides with the length of the body Loudness and pitch: Frequency of vibration determines the shrillness or pitch of the sound. Loudness of sound depends on the intensity of sound and sensitivity of ear. The intensity of sound and hence loudness is measured in decibels (db). Human ears can pick up sound from dB. The loudness is considered to be normal within the range 50-60dB. Humans can tolerate up to 80dB. Beyond this range, it is painful and so considered as undesirable. The sound with loudness greater than 80dB creates noise pollution. The noise pollution is determined not only by loudness but also by its duration. I L. Musical sound: a sound that has a pleasing effect on the ears Natural frequency: The frequency of free oscillation of system Noise: A sound that has an unpleasing effect on the ears Periodic and non-periodic changes: To and fro motion of a ball is called oscillation. If the changes are repeated after a fixed time interval, the changes are called periodic. The changes like formation of hurricane or occurrence of earth quake may occur any time. There occurs no periodicity and hence they are known as non-periodic. Reflection of sound: Sound gets reflected from the smooth surfaces. It follows the law of reflection i.e. angle of incidence is equal to angle of reflection. Resonance: When the natural frequency coincides with the external force frequency, we get resonance. SONAR: Sound Navigation and Ranging Superposition of waves: y = y 1 +y 2 Time period: It is the time required to complete one oscillation Transverse: Crosswise; in a direction at right angles to the length of the object. 7

8 Transverse vibration of a body is that in which the line of oscillation makes an angle of 90 o with the length of the body Ultrasound: The sound whose frequency is greater than hertz..it is not audible to human ears. They are used as diagnostic tools. λ Velocity of wave: v = = nλ T Wave length: λ = vt Parameters related to heat and temperature Absorption of heat: It depends on the mass of body, change of temperature and nature of substance (expressed in terms of specific heat s ). Q = ms( T ) Adiabatic process: It is the process in which no heat is exchanged between the system and the surrounding environment Bi-metallic strip: It is made of equal lengths of steel and copper strips. Boiling is a bulk phenomenon but evaporation is surface phenomenon but both require latent heat. In both the processes liquid gets converted into gaseous state. Interestingly, boiling takes place at fixed temperature but evaporation takes place at all temperatures below boiling point. Rate of vaporization of water increases with temperature, decreases with increase in humidity and increases with increase in wind speed. Calorie and joule: Calorie is the amount of heat required to raise the temperature of one kg of water by 1 o C. Clinical thermometer: It is used to measure body temperature. Its range varies from 35 to 42 o C. Effect of heat: Effects of heat flow are rise in temperature, change in size, change in volume (water expands after 4 o C but it contracts when heated from 0 o c up to 4 o C), increase in pressure, change of state, chemical change, physiological change etc. Efficiency: It is the ratio of output to the input Gas (ideal) equation: p v = RT Heat and temperature: Heat is a form of energy but temperature is the degree of hotness. Heat capacity: It is the amount of heat required to raise the temperature of the body by 1 o C. heat capacity = m s. Isobaric process: The thermodynamic process taking place at constant pressure. Isochoric: The thermodynamic process taking place at constant volume. Isothermal : The thermodynamic process taking place at constant temperature. Latent heat: It is associated with the change of state. The heat given to the system does not increase its temperature. Liquefaction point: It is the temperature at which gaseous state starts converting into liquid state without any change in temperature. Modes of heat transmission: Conduction, convection and radiation 8

9 Recognition of parameters that show temperature dependence: thermal expansion (Mercury and Alcohol thermometers), pressure (Air thermometer), electrical resistance (Platinum resistance thermometer), thermo e.m.f. (Thermocouple, thermopile) etc. Solidification point: It is the temperature at which liquid starts converting into solid state without any change in temperature. Specific heat: It is the amount of heat required to raise the temperature of unit mass of substance through a unit temperature. Temperature (relation between Celsius and Fahrenheit) C 5 32 = F 9 Thermal expansion: The expansion produced in the substance when heated is known as thermal expansion. Thermostat: It is a devise used to control the temperature automatically. Green house: It is used to grow plants in cold weather. Parameters need quantitative expression Standards Measurement Errors Units (C.G.S. and M.K.S. system) Awareness of mathematical tools Graphs: Choosing two variables keeping rest constant; x,t; p,v; v,t etc. Area under the curve Geometry Algebra From geometry to algebra Logarithm Trigonometry Integral and differential calculus Vectors Difference between addition of vectors and numbers Shape and symmetry Groups Criterion of forming groups Parameters need of measurement directly or indirectly Errors in measurement Choosing suitable instrument Least count Quality and Quantity Dimensions One, two and three dimensions: line, plane and solid body Magnitude and direction Studies in Physics Understanding of an event qualitatively 9

10 Knowing the variables and the environment Inputs and outputs Recognition of the scalar and vector nature of the involved quantities Dealing with the parameters Finding interrelations Description of the event Choosing a coordinate systems Formulation of the problem Proceed to solve Approximations Linearity is a good approximation but it fails at number of occasions Newton s laws fail at high speeds Mass is speed independent good approximation in day to day life motion Leaning to Model Knowing the symmetries of the system Ring, disc, shell, sphere, cylinder, Rigid body Black body Ideal and real gas Atom, molecule Monatomic, diatomic and polyatomic Interatomic and intermolecular distances and forces Problem phobia How to get rid of Problem phobia? The student's possess a poor level of problem solving. They are afraid of problems. This is not a good state of affair with the growth of physics education. Merely exposure to the large number of topics is not going to help in making physics as career. Unless and until one has extensive knowledge, he can not be successful. The problem solving skills help in having depth of understanding. The reason being the examination system. Even the autonomous colleges get their paper set from those who are involved in the conventional routine type of examination system. The university examination system is designed to get easy grading. The students can easily guess what is to be expected from them in the examination simply by looking into last two - three years' question papers. The aim of the students is to pass with good marks with or without depth. For them, cramming and memorizing are only important and not the critical thinking and creativity. The heaviness of the course contents encourages them to follow this easy path. For teachers also it is easy to teach with examination point of view. When they teach in examination friendly style, there remains no scope for creativity in the class. In the autonomous colleges, there is flexibility in designing the course contents. It may be remembered that the course contents should provide a general guideline only and should not become Geeta for you because for creativity, flexibility is necessary and you need to go left and right depending upon the level of the class. This flexibility gives scope for the problems to be discussed in the class. This is only the way of teaching science creatively. Further, one should remember that discussion on problems does not mean to solve the problem mathematically step by step. In stead, the various possible approaches need to be discussed leading to thorough understanding of the subjects. The implications of various approaches are to be discussed. There should be flow during teaching but spoon feeding need to be avoided at any cost. This is only the way to bring self-reliance in the students. Simple calculations and obvious steps should intentionally be avoided and should be given as homework to the students. The time saved in this way can easily be invested in developing problem solving skills in the students. 10

11 Further, the preparing, scoring and evaluating the examination must also be done by the same teacher or a board of teachers appointed by the department in which course instructor should be one of the members. This will provide a great deal of flexibility to the teacher in the classroom while teaching. Truly, the major concern of Physics teaching should be to expose the students with the art of probing, observing and analyzing. The examination should be given to test the degree of perfection achieved. The purpose of teaching is to make aware the students of their hidden potential so that they can solve the real life problems that will always be new and in appear during unforeseen circumstances. Study the problem Read the given problem carefully. This will help in thorough understanding of the problem and in extracting what is given and what is to be determined. Following steps may be followed: Find the area in which the problem belongs Recall the background in your memory Set various help levels Split the problem into suitable parts Recognize help levels for each part of the problem Diagnose the problem Make list of the givens. If graph is given, read it carefully and extract all possible information from it. Convert all the units of the given quantities in any one convenient system of units and follow the same throughout. Search for the hidden information: symmetry of the problem: choosing the coordinate system: polar or Cartesian or elliptical or parabolic. Try to get a geometrical picture, which can be used to find relations between various quantities. What is to be determined which can lead to the solution of the problem? Is there any direct relation between the known and unknowns to be determined? Is there any scope for taking any approximation using Bionomial theorem, Taylor's theorem, logarithmic, exponential or sin -cosine series? Make a note. Bionomial theorem can be used to estimate approximate value the square root of any number (1 + x) 1/2, where x <<1, as (1 + x/2). Result and significant figure: In general, in the final result one should not have more significant figures after decimal than in the original data. But the process of rounding off must be done only in the final result and not during the calculation without proper physical justification. Technique to be followed: 1. Look into those direct problems, which require direct application of formula. This is necessary to be familiar with the types of calculations and proper selection of the units required. 2. Look into those direct problems, which require indirect application of formula. This is necessary to inculcate the habit of searching some hidden links. 3. Look into those direct problems, which require some approximations to be considered before applying the formula. This will help in knowing the importance of the terms with physical point view that can affect the results. 4. Start with the problems that require the given situation to be analyzed. Select those problems whose solutions are available but not known to you. Try to find the approach or approaches and attempt solving. Check the answer and compare the approach with that used in the available solution. This is necessary for adjudging the level of understanding you possess and gaining the confidence level. 11

12 5. After gaining confidence, take up unknown type of situational problems and then examine critically the approach. Errors in measurement: Some definitions Instrument: A device/mechanism used to measure the present value of a physical quantity Measurement: The process of determining the amount, degree or capacity by comparision with accepted standards of the system of units Accuracy: The degree of exactness of a measurement compared to the expected or desired value Resolution: The smallest change in the input to which an instrument responds Sensitivity: It is closely related to resolution. It is defined as the ratio of change in output of the instrument to the change of input of measured variable. An instrument may have very good sensitivity but very poor resolution or very small sensitivity but good resolution. Precision (P): It is a measure of repeatability or reproducibility. It gives consistency of instrument output for a given value of input. It is defined as P = 1 Here X n X X n n X n is the average value of X and X n is the value of n th observation. Expected value: The design value or most probable value (Y n ) Absolute error (e): The deviation of the true or measured value (X n ) from the desired value (Y n ) e = X n - Y n Percentage error: e % error = 100 Y n Accuracy (A): 12

13 Error is also expressed as absolute accuracy A = 1 - e Y n This may be expressed as % accuracy. Significant figures: It is the indication of precision of measurement. Let the reading of temperature is 25 o C. This indicates that the reading may vary from 24 to 26 o C. But, if the reading of temperature is 25.1 o C. This indicates that the reading may vary from 24.9 to 25.1 o C. Illustration: 1. The expected value of voltage across a resistor is 80V and the measured value gives 79V. Calculate the absolute error, percentage error, relative accuracy and percentage accuracy. Answers: 1V, 1.25%, , Let us consider following set of 10 observations and calculate the precision of the 6 th measurement. S.No. Measured value (X n ) Average of 10 measurements = 1005/10 = th measurement: 100 Precision = Precision of the 6 th measurement is Errors Static and dynamic errors Static error of any measuring instrument is the numerical difference between true value and the experimentally observed value obtained by measurement. Dynamic errors are related to the sluggishness of the instrument in giving response to the input signal. It is due to inertia, thermal capacitance, fluid capacitance and electrical capacitance. 13

14 This error is important while using industrial instruments. These instruments waits for certain process to take place. These instruments measure the quantities that always fluctuate in time. The dynamic behaviour is determined by subjecting its sensing element to some unknown and predetermined variations (e.g. stepwise changes, linear changes, sinusoidal changes etc.) in the physical quantity. The dynamic characteristics of an instrument are Speed of response Fidelity (faithful reproduction) Lag Dynamic error Sources of error: 1. Insufficient knowledge of process parameters and design condition 2. Poor design 3. Poor maintenance 4. Human involvement in operation 5. Design limitations Types of static error This error may be classified as Gross error Systematic error Random error Gross error: Human mistakes (also carelessness and bad habits) in reading or using instrument (not setting zero) and in recording and calculating. Some gross errors may easily be detected but some are really illusive. These errors can not be treated mathematically. These can be avoided only through practice. Systematic error: These are generally due to shortcomings of instruments. Defective parts, worn parts, ageing effects of the environment on the instrument cause this type of error. This error is of three types; Instrumental error Environmental error Observational error The instrumental errors are due to the mechanical structure of the instruments. Friction in bearing, irregular spring tension, calibration errors etc. creates this type of error. The effects of changing environmental conditions e.g. temperature, pressure and humidity changes. The electrostatic and magnetic field s present may also cause this error. These errors may also be divided as static (due to limitations of measuring device) and dynamic (due to slow responding) errors. 14

15 Random error: These have unknown origin. These are generally due to accumulation of a large number of small effects and may be of real concern if high degree of accuracy is required. They cannot be corrected by any method of calibration or any known method of control. It can not be explained without minute investigations. The only way is to collect a large number of data and then treating them statistically as these errors are due to unknown causes but follow the laws of probability. Statistical treatment of data: For these the systematic error in the data should be as small as possible as compared to random errors. The statistical treatment can not remove a fixed bias contained in all the measurements. Arithmetic mean: The most probable value of a measured variable is the arithmetic mean. It is defined as _ x 1 +x 2 +x 3 xn x = n Deviation from mean: It is the departure of the given reading from the arithmetic mean. For example, the deviation of the first reading from mean, d 1, is _ d 1 = x 1 - x Here a proper sign is used to express deviation. However the expression of the absolute value of deviation requires no sign. If there are ten readings for an observation, there will be ten deviations (d 1, d 2,.d 10 ) from the arithmetic mean. By taking any suitable example, it can easily be demonstrated that the sum of all the deviation equals zero. Average deviation: It is an indication of the precision of the instrument employed. It is defined as the average of absolute value of all the deviations for the readings of the observation Variance or mean square deviation: it is the mean of all squared deviations (d 2 1, d 2 2,.d 2 10 ) from arithmetic mean. It is expressed by the symbol σ 2. Root mean square or standard deviation: it is the square root of the sum of all the individual deviations squared (d 2 1, d 2 2,.d 2 10 ) divided by total number of readings (n) for infinite number of readings. But if the readings are finite in number, then the sum of all the individual deviations squared (d 2 1, d 2 2,.d 2 10 ) is divided by (n-1) and not by n in order to get standard deviation. It is expressed by the symbol σ. Probability of errors: normal distribution of errors The result of a series of measurements can be presented can be presented graphically in the form of a block diagram or histogram in which the number of observations (frequencies of occurrence) are plotted against the readings of measured physical quantity. Say for example, we have following table for the 50 readings during current measurement in a circuit Readings (in ampere) Frequency of occurrence

16 (most frequently occurred) The largest frequency occurs at the central value corresponding to 56.4 ampere. The others are more or less placed symmetrically around this value. If more readings are taken at smaller increment (say 0.05), the distribution would be observed to be more symmetrical (better than previous). A large number of data at still smaller increment will result into a very smooth bell-shaped curve in the plot. The contour of the histogram is perfectly symmetric. The bell-shaped curve is known as Gaussian curve. The sharper and narrower Gaussian curve implies that the central value is most probable value of the true reading. The Gaussian or normal law of error forms the basis of the analytical study of random effects. According to this law: 1. All observations include random error (due to small perturbing effects of unknown origin) 2. Random errors can be positive or negative 3. There is equal probability for positive and negative random errors. The error distribution curve (Gaussian probability curve) is obtained by plotting error function (in terms of σ) against the occurrence of the readings. The curve based on normal law shows a symmetrical distribution of errors. It extends from - to +. The area under the curve between + σ to σ represents the cases that differ from the mean by no more than standard deviation. Probable error: In the curve find the limits of error function that includes half the cases. This limit gives probable error. The probable error is used in experimental work in the past. However the standard deviation is preferred as it is more convenient in statistical work. Limiting errors: Look at the instruments. Manufacture gives a guarantee of accuracy. Similarly, look at electronic components. They are guaranteed within a certain percentage of their rated value. The limits of the deviations marked on the instrument (as provided by manufacturer) are known as limiting errors (or guaranteed errors). 16

17 bdkbz & 1 ekiu,oa lfn'k&vfn'k HkkSfrdh gs D;k\] izkphu Hkkjr esa ekiu] osx ladkj] flfkfr LFkkidrk laldkj] xq:ro rfkk xq:rokd"kz.k] vfn k rfkk lfn k] lfn kksa dk fo;kstu] f}in izes;] ekiu esa =qfv;k A izlrkouk fokku dk 'kkfcnd vfkz gs fof'k"v KkuA fokku 'kcn dh O;qRifÙk ysfvu Hkk"kk ds 'kcn **Scientia** ls gqbz ftldk vfkz gs **tkuuk** Kku dk laca/k tkuus ls gksrk gsa lald`r 'kcn **fokku** vksj vjch 'kcn **bye** lekukfkhz 'kcn gsa ftudk vfkz gksrk gs **laxfbr Kku**A izd`fr vksj izkd`frd?kvukvksa ds Øec) izs{k.kksa,oa iz;ksxksa ls izkir Kku dks fokku dgrs gsa rdz vksj iz;ksx fokku ds egroiw.kz vkstkj gsa fokku dh 'kk[kk, & vk/kqfud ;qx esa fokku ds rsth ls fodkl o v/;;u dh lqfo/kk ds fy, bls eq[;r;k nks 'kk[kkvksa esa fohkkftr fd;k x;k gs& HkkSfrdh; fokku ¼Physical ¼ Science½& blds vurxzr HkkSfrdh] jlk;u fokku] [kxksy fokku] vkfn fo"k;ksa dk v/;;u fd;k tkrk gsa thofokku ¼Biological ¼ Science½& blds vurxzr thofokku] oulifr fokku vkfn fo"k;ksa dk v/;;u fd;k tkrk gsa ;gk ij ge dsoy HkkSfrd 'kkl= ds ckjs esa ppkz djsaxsa 1- HkkSfrdh gs D;k \ jkf= dk vkdk k ns[kks & jks kuh esa ugk jgs 'kgj esa ugha xk o esa jg dj ns[kksa izd`fr dh xksn esa csb dj ns[kksa unh] igkm+ vksj lkxj dh vksj ns[kksa izd`fr esa?kv jgh?kvukvksa dks ns[kksa euksgkjh n` ;ksa dks ns[kks vksj izy;adkjh n` ;ksa dks Hkh ns[kksa ukuk izdkj ds inkfkksza dks ns[kksa muesa O;kIr lefefr vksj lqunjrk dks ns[kksa muls fc[kj jgs jaxksa dks ns[kksa vius vklikl ds okrkoj.k dks /;ku ls ns[kks vksj /;ku ls lquksa vkidks vius okrkoj.k esa inkfkz] ÅtkZ] dky vksj vkdk k i`fkd&i`fkd fn[kkbz nsaxsa /;ku ls ns[kus vksj lquus ls vkidks vyx&vyx fn[kkbz ns jgh?kvukvksa esa varzlecu/k feyrs utj vkus yxsaxsa 17

18 /;ku ls ns[kuk] /;ku ls lquuk vksj varlzecu/kksa dks [kkstuk gh HkkSfrdh gsa ;g lc,d ftkklq gh dj ldrk gsa vr% ftkklq gksuk HkkSfrdh ds v/;;u gsrq tqvus vksj mlesa lqyrk ikus dh igyh 'krz gsa fdlh Hkh?kVuk ds flyflysokj v/;;u ¼pkgs og ls)kafrd rjhds ls gks ;k izk;ksfxd rjhds ls gks vfkok nksuksa gh rjhdksa ls gks½ ls le> isnk gksrh gsa le> ls Kku isnk gksrk gsa rfkk Kku ls fo ys"k.k djus] fu;a=.k djus] la kksf/kr djus vksj iwokzuqeku yxkus dh {kerk fodflr gksrh gsa iwokzuqeku [kkst&dk;z dks vkxs c<+krs gsa ftlls fokku izxfr djrk gs vksj lekt dks leiuu cukus dk jklrk feyrk gsa HkkSfrdh esa dqn Hkh vafre fl)kar ds :i esa ugha gksrka tks vkt lp dk vkhkkl ns jgk gs] gks ldrk gs fd dy og xyr lkfcr gks tk;sa D;k vkidks dqn ;kn vk jgk gs\ gk! ;kn dhft;s dksijuhdl] xsfyfy;ks] U;wWVu] Iykad] MkYVu] VkWelu] jnjqksmz vkfn dksa HkkSfrdh esa dk;z djus dh nks fn kk;sa gsaa fdlh Hkh?kVuk ;k fudk; dks Åij ls uhps ;k uhps ls Åij tkrs gq, le>uka bl rjg HkkSrdh esa fdy"v fudk; dks fgllksaa esa ck Vuk vksj fqj fgllksa dks le> dj iwjs fudk; dks le>uk gksrk gsa HkkSfrdh esa v/;;u djrs gq, oskkfudksa dks pkj ewyhkwr cyksa dh tkudkjh feyha nks nzo;&fi.mksa ds chp fdz;k khy cy dks xq:rokd"kz.k cy dgrs gsa pkgs os nzo;&fi.m vfrlw{e d.k gksa vfkok fo kkydk; czãk.mh; fi.m gksaa nzo; esa ftu HkkSfrd vksj jlk;fud xq.kksa dh l`f"v gksrh gs] mlds ihns ftl cy dk gkfk gksrk gs mls fo qrpqecdh; cy dgrs gsaa fofhkuu rroksa ds fuekz.k ds ihns fdz;k khy cy dks ukfhkdh; cy dgrs gsa tks nks izdkj ds gksrs gsaa vkt oskkfud ml ewyhkwr,dhd`r ije cy dks tkuuk pkgrs gsa tks lhkh izdkj ds cyksa dh mrifrr dk dkjd gksa oskkfudksa dh ;g [kkst&;k=k ekuo tkfr ds dy;k.k ds fy;s u;s lk/ku tqvkus vksj viuh Lo;a dh {kq/kk dks 'kkar djus dk vuojr iz;kl gsa HkkSfrdh ds v/;;u ls dbz,sls fu"d"kz fudys gsa ftugksaus rduhdh fodkl ds jklrs [kksys gsaa rduhdh fodkl us u flqz lekt ds fodkl esa viuh vge~ Hkwfedk fuhkkbz gs oju~ HkkSfrdh o vu; {ks=ksa esa v/;;u gsrq u;s lk/ku Hkh tqvk;s gsaa vkt,slk dksbz Hkh {ks= ugha gs tgk HkkSfrdh dh enn u yh tkrh gksa vr% HkkSfrdh dk v/;;u dj fdlh Hkh {ks= esa lqyrk dh uhao dks iq[rk fd;k tk ldrk gsa 18

19 2- izkphu Hkkjr esa ekiu& fo'o ds izkphure xzfkksa esa osnksa dk uke myys[kuh; gsa ;g gekjs izkphu Hkkjr esa xksjoiw.kz dky dk nlrkost gsa ;g ns'k dh oskkfud rfkk lkald`frd Å apkbz;ksa dh >yd nsrk gsa bldk izhkko rkrdkfyd lald`fr;ksa] tsls fd felz] if'kz;k rfkk vjc lald`fr esa fn[krk gsa izkphu Hkkjr esa yeckbz] le;] rkieku rfkk nzo;eku ds iw.kzfodflr ekiu ds ek=d FksaA bldk laf{kir ifjp; fueukuqlkj gs& 2-1 yeckbz dk ek=d % ^n.m* _Xosn ¼4500&2500BC½ rfkk HkkLdjkpk;Z }kjk jfpr izkphu xzafk ^^lw;z fl}kur** ds vuqlkj izkphu Hkkjr esa iz;qdr gksus okys yeckbz ds ek=d rfkk O;qRiUu ek=d fueu Fks 8 ijek.kq = 1 =ljs.kq 8 =ljs.kq = 1 js.kq 8 js.kq = 1 ckykxz 8 ckykxz = 1 fy[; 8 fy[; = 1 ;qd 8 ;qd = 1 ;o 8 ;o = 1 vaxqy 24 vaxqy = 1 glr 4 glr = 1 nam 2000 nam = 1 Øks'k 4 Øks'k = 1 ;kstu _Xosn dh igyh _pk bl yeckbz ds ek=d ^n.m* ¼tks fd yxhkx 1 ehvj yeckbz esa Fkk½ dk i`foh dh ifjf/k ls lecu/k crkrh gs tks fd fueu gs& S = 1000X 2000 X 2000 X 24 vxaqy 25 = 24 X 10 9 X 1 ^n.m* = 4 X 10 7 n.m tks fd yxhkx i`foh dh ifjf/k 4 X 10 7 ehvj ds cjkcj gsa vfkkzr n.m gekjs vk/kqfud yeckbz ds ek=d ehvj ls yxhkx leku FkkA 19

20 HkkLdjkpk;Z ¼ tue 1114 bz-½ }kjk jfpr izkphu xzafk ^lw;z fl}kr esa i`foh dh f=t;k vkb lks ;kstu crk;h xbz gs bl izdkj i`foh dh ifjf/k S = 2π X 800 ;kstu = 2π X 800 X 8000 n.m = 4-02 X 10 7 n.m gh izkir gksrh gsa rks bl lekurk ls ge,d vaxqy dks 1@96 ehvj eku ldrs gs 1 vaxqy = ls-eh- rfkk,d ijek.kq = ¼8½ &7 vaxqy = 5 X 10 &7 ls-eh- = 5 A 0 tks fd fdlh ijek.kq ds eki ds yxhkx cjkcj gsa nzo;eku dk ek=d % ^ek"k* ^pjd lafgrk* esa of.kzr nzo;eku ds ek=d fueu FksA 10 d`".ky = 1 ek"k 10 ek"k = 1 lqo.kaz 32 ek"k = 1 jksi;@rkeziy = 10?kkj.k 48 ek"k = 1 yksgiy = 10 eqf"v 300B.C. esa dksfvy; us vius xzafk ^vfkz'kkl=* esa Hkkj ds ek=d dh lfolrkj foospuk dh gsa 2-3 le; dk ek=d % ^gksjk* izkphu Hkkjr esa ^lkou* ekiu i}fr le; dh x.kuk ds fy, izpfyr FkhA blds ek=d o O;qRiUu ek=d Hkh iz;ksx esa FksA 60 foiy = 1 iy 60 iy = 1?kVh 2 ψ?kvh = 1 gksjk 24 gksjk = 1 lkou fnu@lksj fnol@u{k= fnu ^lw;z fl}kur* esa of.kzr,d o"kz dh vof/k 365¼ fnu dh ekuh xbz gs ¼365 fnu@15?kvh@30 iy½ tks fd gekjs vk/kqfud o"kz dh x.kuk ls esy [kkrh gsa izkphu Hkkjr esa ^gksjk* dk vk/qkfud :i ^Hour* gsa 20

21 blds vfrfjdr lw;z fl}kur esa uks vu; ekiu ds ek=d izpyu esa FksA ftuesa ls fueu izeq[k gs& 1½ 1 czã o"kz = 200 dyi 1 dyi = 1000 egk;qx 1 egk;qx = ¼4800$3600$2400$200½ fno; o"kz = lr;qx $ =srk;qx$nzkij$dkfy;qx = 12]000 fno; o"kz = 4]32]000 lksj o"kz 2½ 1 fno; o"kz = 360 lksj o"kz 3½ 1 lksj o"kz = 365¼ lkou fnu ;k u{k= fnu 4½ 1 xksjo = 60 lksj o"kz 5½ 1 izktkir; ¼eUoUrj ½ = 71 egk;qx 6½ 1 fir`fnu = 1 pkunzekl 2-4 rkieku dk ek=d % ^fyad* os'ksf"kd n'kzu esa ^Li'kZ* B.Mk rfkk xez dk,glkl djkrk FkkA 'kcn ^Li'kZ* vk/kqfud HkkSfrdh ds Temperature ¼rkieku½ ds leku FkkA m".krk dks ekius ds fy, ^ m".k Li'kZ* ek=d Fkk blesa ikuh ds teko fcunq dks B.Mk ekurs gq, vf/kdre rki ikjs ds ;k lksus ds xyu fcunq dks ekurs FksA bu nksuksa vyx vf/kdre rki fcunqvksa ij fuhkzj nks ek=d izpyu esa Fks i) fyad Fks& 1 izfyad = 1 iknd{; = C 4 iknd{; = 1 d{; = C 6 d{; = 1 fyad = C ii) d{; 1 ;g nksuksa vkil esa fueu izdkj lecfu/kr 113 iknd{; = ikuh dk Hkki fcunq ¼B.P.½ = C 101 d{; = ikjs dk B.P. = C 50 fyad = lksus dk xyu fcunq ¼M.P.½ = C lunhkz iqlrds& 1- Indian Heritage of Science and Technology The Physis by Dr. N.G. Dongre 2- Samskrita Bharti, New Delhi. 21

22 3- iz'klrin Hkk"; rfkk U;k;dUnkyh 4- Prashasta Pada Bhashya With Nyayakandali of Shridhara Pulised by E.J. Lazarus and Co., Benares: Kautileya Artha Shastra- (Ed) R.P. Kangle, Motilal Banarsidas Publishers Pvt. Ltd Amshu Bodhine Of Maharishi Bhardwaja. 7- Surya Siddhanta (Ed) with Tattvamitra Sanskrit Commentary, Pub Jaiykrishna das Haridas Gupta Benaras City Vaisheshika Sidhantanam Ganitiya Paddhatya Vimmarshah-Dr. Narayan Gopal Dongre, Pub., Director, Reseanch Instilute, Sampunanda Sanskrit Vishvavidyalya, Varanas Physics Ancient India (A Mathematical Analysis of Vaisheshida Philosophy), N.G. Dongre Pub. Wiley Eastesn Limited (New Age Int. Pub. Ltd) osx laldkj& _f"k d.kkn }kjk ^os'ksf"kd lw=* dh jpuk dh xbz Fkh rfkk mlesa iz'klrin Hkk"; esa *osx laldkj* ¼Mechanical Force½ dk o.kzu gsa os'ksf"kd fl}kur esa of.kzr 'kcn ^dez* dks lkeku; xkfr ¼Motion ½ ds fy, iz;ksx fd;k x;k Fkk rfkk ^osx* 'kcn Force ¼cy½ ds vfkz esa iz;qdr gksrk Fkk vfkkzr fdlh olrq ij ^osx* ds iz;ksx ls ^dez* izkir gksrk FkkA ^xeudez* fdlh olrq ds Momentum vfkkzr laosx dks n'kkzrh FkhA Velocity ds fy, ^xfr* 'kcn dk iz;ksx gksrk Fkk ^js[kh; rfkk ^o`ùkh; xfr* dk lfolrkj myys[k izkphu [kxksyfokku ds xzufkksa esa feyrk gsa ^fnd* 'kcn fn'kk dk Kku djkrh FkhA fnd~ lfn'k jkf'k Fkh rfkk Roj.k ¼Acceleration½ ds fy, ^osxp;* 'kcn iz;qdr fd;k tkrk FkkA ^osx laldkj* dk o.kzu djus okys okd; ls fueu xfr ds fu;e izkir gksrs Fks 1- ^osx* ds iz;ksx ds ^dez* mriuu gksrk gsa 2- ^dez* ds ifjorzu ^osx* ds lekuqikrh gksrs gs rfkk og osx dh fn'kk esa gksrs gsa 3- izr;sd la;ksx ¼Action½ ds fy,,d fojks/kh rfkk cjkcj Reaction osx gksrk gsa vfkkzr nks olrqvksa dk,d nwljs ij ^osx* la;ksx cjkcj rfkk fojks/kh fn'kkvksa esa yxrk gsa blh izdkj ge bl lunhkz xzafk ls js[kh; xfr ds lhkh lw= izkir dj ldrs gsa tsls fd v = u + at rfkk v2= u2 + 2as dez Hkh pkj izdkj ds ekus x;s Fks 22

23 1- mr{ksi.k ¼ mr{ksi.k ¼upward motion½ 2- vo{ksi.k ¼ vo{ksi.k ¼downward motion½ 3- vkdqapu 4- izlkj.k ¼ apu ¼motion due to tensile stress½ izlkj.k ¼Shear freed motion½ 4- flfkfr LFkkidrk laldkj ¼Elastic ¼ Forces½ os'ksf"kd n'kzu esa elasticity dks flfkfrlfkkidrk dgk x;k gsa bldk o.kzu U;k; dunyh ds,d 'yksd esa dqn bl izdkj gs& rkieku dh rjg Bksl olrqvksa esa flfkfrlfkkidrk dk Hkh xq.k gksrk gs rfkk bl xq.k ds dkj.k Bksl olrqvksa esa] cy yxkus ij tks fo:i.k gksrk gs mlls] okfil viuk vkdkj izkir dj ysrh gsa djdkoyh esa elasticity ¼izR;kLFkrk½ dks fueu izdkj le>k;k x;k gs& elastic forces Bkslksa rfkk vn`'; inkfkksz esa mriuu gksrs gs rfkk blh dkj.k inkfkz Vibrate ¼dfEir½ gksrs gsa 5- xq:ro rfkk xq:rokd"kz.k& os'ksf"kd n'kzu ds vuqlkj xq:ro gh Bksl rfkk nzo; dk uhps dh vksj fxjus dk dkjd gsa ;g vn`'; gs rfkk inkfkksz ds fxjus ls gh bldk Hkku gksrk gsa rfkk xq:ro dk Kku Bkslksa dh Hkhrjh vkurfjd d.kksa ds eki ij fuhkzj gsa ^U;k;dUnyh* ds o.kzu ds vuqlkj xq:ro ds dkj.k Bkslksa dk izr;sd d.k,dleku :i ls uhps fxjrk gsa vfkkzr,d cm+h olrq rfkk,d NksVh olrq,dleku :i ls xq:ro ds dkj.k uhps fxjrh gsa tcfd if'peh ns'kksa esa vjlrq ds fl}kur ls olrqvksa ds uhps fxjus dh nj dk olrqvksa ds Hkkj ds lekuqikrh ekuk tkrk Fkk vfkkzr Hkkjh olrq tynh uhps fxjsxh rfkk gydh olrq nsj lsa lu~ 1590 esa xsfyfy;ksa us ;g fl) fd;k fd lhkh olrq, xq:ro ds dkj.k,d leku xfr ls uhps fxjrh gs] exj ;g fl}kur izkphu Hkkjr esa _f"k d.kkn ds os'ksf"kd n'kzu esa ekstwn FkkA,d vu; 'yksd esa ;g crk;k x;k gs fd i`foh dh lrg ij izr;sd olrq i`foh ds dsunz dh vksj tkrh gqbz js[kk dh fn'kk esa fxjrh gsa HkkLdjkpk;Z ¼1134 bz-½ ds vuqlkj i`foh esa viuh vksj [khapus dh {kerk gs rfkk,d Hkkjh fi.m ¼xq:½ tks czãekam esa miflfkr gs vius Hkkj ds lekuqikr ¼xq:Ro½ esa i`foh dks [khprk gsa vfkkzr czgekam dh izr;sd olrq,d nwljs dks viuh vksj [khaprh gsa blh izdkj [kxksyh; fi.mksa dh xfr fokku rfkk mudh lvhd x.kuk,a vusd izkphu xzafkksa esa myysf[kr gsa lanhkz iqlrd&physic in Ancient India (A Mathematical Analysis of Vaisheshika Philosophy)- N.G. Dongre Pub., Wiley Eastern Limited (New Age Publishers Limited)