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1, PHYSICS, CLASS –XI, Unit-1, PHYSICAL WORLD AND MEASUREMENT ----------------- 3 marks, Physics:, It is the branch of physics which deals with nature and natural physical, phenomena., FUNDAMENTAL FOURCES IN NATURE, 1. GRAVITATIONAL FORCE:, Every body in this universe attracts every other body with a force known as, gravitational force. According to Newton, the force of attraction between every, pair of particles or bodies is directly proportional to the product of the masses, of the particles (or bodies) and inversely proportional to the square of the, distance between these particles or bodies., Consider two particles A and B masses m1 and m2 respectively. Let ‘r’, be the distance between these particles as shown in figure 1., Accordingly to Newton’s law of gravitation,, F α m1 m2 --------------------------- (1), and F α 1/r2, (2), Combining eqns. (1) and (2), we get, F α m1m2/r2 or F = Gm1m2/r2 -------------- (3), Where G= 6.67 X 10-11 Nm2 kg-2 is known as universal gravitational constant., Eg: - The moon orbits around the earth is due to this force., , Properties of gravitational force, 1.Gravitational forces are equal in magnitude but opposite in direction., 2.It is a central force i.e., it acts along the line joining the centres of the, two interacting bodies., 3.It does not depend upon the presence of other bodies., 4.It is a long range force i.e.,it is effective even if their distance of, separation is very large., 2. ELECTROMAGNETIC FORCE :, It is the force between charged particles., If the charges are at rest then it is called electrostatic force., Eg:- The motion of an electron around the nucleus., Properties, 1. It is both attractive and repulsive., 2. It is a long range force., 3. It is a central force., 4. It is 1036 times stronger than the gravitational force., 3. STRONG NUCLEAR FORCE :, The force holding the protons and neutrons inside a nucleus is known as, strong nuclear force., Eg: - A nucleus and hence atom can exist if there is a strong nuclear force, between the proton and neutron.
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2, Properties, 1. It is attractive in nature., 2. It acts over a very short range., 3. It is 100 times stronger than electromagnetic force and 1038 times, stronger than gravitational force., 4. WEAK NUCLEAR FORCE :, The force between an electron and a neutrino is known as weak nuclear force., In β-decay, electron and a neutrino (uncharged particle) are emitted., Properties, 1.It is 1025 times stronger than the gravitational force., 2.It operates only through a range of nuclear size (≈ 10-15m)., Isolated system, Any system on which no external force scts., Nature of physical laws, The various phenomena occurring in nature are explained on the basis of certain, laws. Theses laws are expressed in terms of some physical quantities., 1. Law of conservation of electric charge, According to this law, the total charge on an isolated system remains constant., , eg, If an uncharged glass rod is rubbed with an uncharged silk cloth ,the, glass rod becomes positively charged and the silk cloth becomes, negatively charged. The positive charge on the glass rod is equal to the, negative charge on the silk cloth., Here,total charge on the system(glass rod +silk cloth) before rubbing = zero, Total charge on the system after rubbing = zero,, which is the law of conservation of charge., 2. Law of conservation of energy, According to this law, energy can neither be created nor destroyed but it, can be changed from one form to another., E.g., The total energy (i.e. kinetic energy + potential energy) of a freely falling, body remain constant., 3.Law of conservation of linear momentum, This law states that, if no external force acts on a system, then its linear, momentum remains constant., E.g., rocket propulsion, 4.Law of conservation of angular momentum, It states that if no external torque acts on a system, then its angular, momentum remains constant., E.g. while revolving in its elliptical orbit, when a planet approaches the sun, its, moment of inertia about the sun decreases. To conserve the angular momentum, its, angular speed increases., 5.Law of conservation of mass-energy, According to this law, mass of a system can be converted into energy and, energy of a system can be converted into mass i.e. mass and energy are interconvertible quantities. It is given by,, E =mc2, where m=mass, E=energy, c= speed of light in air/vacuum., e.g. Nuclear Reaction.
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3, PHYSICAL QUANTITY :, A quantity which can be measured directly or indirectly is called a physical, quantity. Eg:- mass of a body, length of an object, time of an event, velocity,, acceleration, momentum etc.., UNIT:, Unit is a standard quantity with which a physical quantity of same kind is, compared for measuring it., For the measuring of a physical quantity (say x), two things are required., i) The unit (u) in which the physical quantity is expressed., ii) The number [or numerical value (n)] of times the given unit is contained in the, physical quantity. i.e. Physical quantity = number X unit, Or X = nu, Example : Length of a rod = 4 meter., It means, the length of a rod (i.e. Physical quantity) is 4 times a meter the unit of, measuring length., FUNDAMENTAL QUANTITIES:The quantities mass, length and the time are called fundamental quantities and, their units are known as fundamental units or base units., Eg:- length, mass, time.., FUNDAMENTAL UNITS : The units of measurement of length, mass and time are called fundamental units, or base units., Or, Fundamental units are those units which can neither be derived from one, another nor can they be further resolved into any other units., Eg:- m, kg, sec.., DERIVED QUANTITY:Any physical quantity which can be derived from the fundamental physical, quantities by multiplying or dividing them is called derived physical quantity., Eg:- speed, acceleration., DERIVED UNITS :The units of measurement of all other physical quantities which can be obtained, from fundamental units., Eg:- Speed, = distance/time, Unit of Speed, = unit of distance/unit of time, = m/s, SYSTEM OF UNITS, 1. The CGS System:, In this system, the unit of length is Centimetre (cm), the unit of mass is Gram, (g) and the unit of time is Second (s)., 2. FPS system or the British System:, In this system, the unit of length is foot, the unit of mass is pound and unit of, time is second., 3. MKS System:, In this system, the unit of length is metre (m), the unit of mass is kilogram (kg), and the unit of time is second (s).
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4, , 4. SI unit (Le System International d’ units):, This system is the modified form of MKS system and hence is also known as, Rationalized MKS system., SEVEN FUNDAMENTAL OR BASE UNITS OF SI., physical quantity, , Name of unit, , Symbol, , mass, , kilogram, , kg, , length, , meter, , m, , time, , second, , s, , temperature, , Kelvin, , K, , physical quantity, , Name of unit, , Symbol, , amount of substance, , mole, , mol, , electric current, , ampere, , A, , luminous intensity, , candela, , cd, , SI SUPPLEMENTARY UNITS, PHYSICAL QUANTITY, Plane angle, Solid Angle, , UNIT, NAME, Radian, Steradia, n, , UNIT SYMBOL, rad, sr, , 1. Radian (rad): It is the unit of plan angle., One radian is an angle subtended at the centre of circle by an arc of length, equal to the radius of the circle., 2. One steradian (sr) :, One steradian is solid angle subtended at the centre of sphere by its surface, whose area is equal to the square to the radius of the sphere., ADVANTAGES OF SI, i) It is a coherent system of units (i.e. all the derived units can be obtained by, multiplying or dividing the certain set of basic or fundamental unit.), ii) It is a rational system of units (i.e. it uses only one unit for a given physical, quantity) eg :- joule is the unit of all forms of energy in SI.
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5, iii) This system of unit is metric system (i.e. all multiples and sub multiples can, be expressed as powers of 10)., iv) This system of unit is internationally accepted., v) This system is closely related to CGS system as SI units can be easily, changed to CSS units., vi) In SI, the total number of units are small., PRACTICAL UNITS OF LENGTH, For large measurement :1. ASTRONOMICAL UNIT (AU) :The average distance between the earth and the sun is called, Astronomical unit., 1 AU =1.496X1011 m, =1.5 X1011m, 2. LIGHT YEAR (ly) :The distance travelled by light in vacuum in one year is called light year., =3X108 ms-1X365X24X60X60, =9.46X1015m, 3. PARSEC (PARALLACTIC SECOND) :It is the distance at which an arc of length equal to one astronomical unit, subtends an angle of one second., , Therefore, 1 parsec, = 3.084 X 1016 m ≈ 3.1 X 1016 m, The distance between stars is usually expressed in parsec., RELATION BETWEEN LIGHT YEAR (ly) AND ASTRONOMICAL UNIT (AU)., We know, 1 light year (ly), =9.46X1015 m, 11, 1 AU = 1.5 X 10 m, Dividing, we get, 1ly, =9.46X1015 m, 1AU, 1.5x1011m, =6.3 x104, Therefore, 1ly, =6.3X104 AU, RELATION BETWEEN LIGHT YEAR (ly) AND PARSEC., We know, 1 parsec, =3.1X1016 m, 1ly, =9.46 X1015 m, 1 parsec, =3.1X1016 m, 1ly, =9.46 X1015 m, = 3.28
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6, , Therefore, 1 parsec, =3.28 ly, Since, 1ly, = 6.3X104 AU, 1 parsec, = 3.28 X 6.3 X 104 AU, Therefore, 1 parsec, = 2.07 X 105 AU, PARALLAX:, Parallax is a displacement or difference in the apparent position of an object, viewed along two different lines of sight, and is measured by the angle or semi-angle of, inclination between those two lines. Due to foreshortening, nearby objects show a larger, parallax than farther objects when observed from different positions, so parallax can be, used to determine distances., To measure large distances, such as the distance of a planet or a star from Earth,, astronomers use the principle of parallax. Here, the term parallax is the semi-angle of, inclination between two sight-lines to the star, as observed when Earth is on opposite, sides of the Sun in its orbit., , FOR SMALL MEASUREMENTS. The following units are used for measuring very, small distances., i) Micron (µm) : One micron is equal to 10-6 m or 1 µm = 10-6 m, ii) Nanometer (nm) : It is equal to 10-9 m or 1 nm = 10-9 m, iii) Angstrom (Å) : One angstrom is equal to 10-10 m or 1 Å = 10-10 m, iv) Fermi : It is the unit of length in which the size of nucleus is measured., 1 fermi (fm) = 10-15 m, For measuring extremely small area, the unit used is barn., 1 barn = 10-28 m2, ACCURACY:, The closeness of the measured value to the true value of physical, quantity. Or;, The accuracy of a measurement is a measure of how close the measured value is, to the true value of the quality., PRECISION :Precision means the extent or limit to which the measurement of a physical, quantity is done., Precision tells us to what resolution or limit the quality is measured by a, measuring instrument., Errors in Measurement:, It is the difference between true actual value and the measured of value of, quantity is known as error of measurement.
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7, Types of Errors:, i) Systematic errors, The systematic errors are those errors that tend to be in one direction, either positive, or negative. Basically, these are the errors whose causes are known., Systematic error are of 4 (Four) types:(a) Instrumental errors:, These errors arise from the errors due to imperfect design or calibration of the, measuring instrument, zero error in the instrument, etc., (b) Imperfection in experimental technique or procedure, To determine the temperature of a human body, a thermometer placed under the, armpit will always give a temperature lower than the actual value of the body, temperature. Other external conditions (such as changes in humidity,, temperature, wind velocity, etc.) during the experiment may systematically affect, the measurement., (c) Personal errors, Such errors arise due to an individual’s bias, lack of proper setting of the, apparatus or individual’s carelessness in taking observations without observing, proper precautions, etc., (d) Natural errors, The errors arising due to the change in the conditions of the environment, (pressure, temp, wind etc.), e.g. expansion of a scale due to increase in temperature., ii) Random errors, The random errors are those errors, which occur irregularly and hence are, random with respect to sign and size. These can arise due to random and, unpredictable fluctuations in experimental conditions (e.g. unpredictable, fluctuations in temperature, voltage supply, mechanical vibrations of, experimental set-ups, etc), personal (unbiased) errors by the observer taking, readings, etc. For example, when the same person repeats the same, observation, it is very likely that he may get different readings everytime., iii) Constant error, When the result of a series of observations are in error by the same amount,, the error is said to be a constant one., ABSOLUTE ERROR:The difference of the true value (standard value) and the observed value, (experimental value) of a physical quantity is called absolute error., It is denoted by x, i.e., absolute error = true value – observed value., Let a physical quantity be measured n times. Let the measured values be x1, x2, x3,, .......xn, then mean, xmean = x1 + x2 + x3 + ........xn, n, Let, xmean = mean value of the measured quantity., xi = value of the quantity measured in ith observation., Therefore, absolute error of the ith observation is given by xi = xmean-xi, ΔXi may be positive or negative., But the magnitude of |ΔXi| is always positive.
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9, (C) ERROR IN CASE OF A MEASURED QUANTITY RAISED TO A POWER:, Suppose Z = A2, Then ,, ΔZ/Z = (ΔA/A) + (ΔA/A) = 2(ΔA/A), Hence, the relative error in A2 is two times the error in A., In general, if, Z = Ap Bq/Cr, Then, ΔZ/Z = p (ΔA/A) + q (ΔB/B) + r (ΔC/C), Q. The time period of oscillation of a simple pendulum in an experiment is recorded, as 2.56 s, 2.62 s, .70 s, 2.58 s, 2.45s respectively. Find the time period, absolute, error in each observation and the percentage error., Solution, , :-
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10
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11, , Q. A physical quantity X is related to four measurable quantities a, b, c and d, as follows:, P = a2b3c5/2 d-2, The percentage error of measurement in a, b, c and d are 1 %, 2 %, 3 % and 4, % respectively. What is the percentage error in the quantity X?, Solution : -, , DIMENSIONS OF A PHYSICAL QUANTITY:, The seven fundamental or base quantities chosen SI are called seven dimensions of, the physical world. They are denoted with [] (square brackets). Thus the length is, represented by [L], mass by [M], time by [T], electric current by [A], temperature by, [K], luminous intensity by [cd] and quantity of matter by [mol]., Note: Using the square brackets [] round a quantity means that we are dealing with, the dimensions of the quantity., DIMENSIONS:, The dimensions of a physical quantity are the power to which the fundamental, quantities are to be raised to represent that physical quantity., Or;, The number of times of fundamental quantity contained in the given derived physical, quantity is known as the dimension., Eg:- area = lXbXh, = [L] X [L], = [L2] i.e. [M0L2T0], The dimensions of area are zero in mass, two in length and zero in time., Eg :- velocity, =, [V], , =, = [LT-1], = [M0LT-1]
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12, DIMENSIONAL FORMULA :The expression which shows that which of fundamental quantities and with, what powers enter into the derived unit of physical quantity., Or;, It may be defined as expression that indicates which of the fundamental units, of mass, length and time enter into the derived unit of that quantity and with, what power., Eg:- volume, = length X breadth X height, = [L3], = [M0L3T-0], Here [M0L3T-0] is the dimensional formula of volume., DIMENSIONAL EQUATION :The equation obtained by equating the symbol of a physical quantity with its, dimensional formula is called dimensional equation., Eg:- [A], = [M0L2T0], Where [A] means area, PRINCIPLE OF HOMOGENEITY :According to this principle, the dimensions of the fundamental quantities of two, sides of a physical relation must be same, Eg:- [MaLbTc], = [MxLyTz], i.e. a = x; b=y; c=z, Or;, According to this principle only that formula is correct, in which the dimensions of, the various terms on one side of the relation are equal to the respective dimensions, of these terms on the other side of the relation., FOUR TYPES OF QUANTITIES :OR:, Different types of variables and constants, 1. DIMENSIONAL VARIABLES :The physical quantities which possess dimensions and have variable values, are called dimensional variables., Eg:- area, volume, velocity etc., 2. DIMENSIONLESS VARIABLES :The physical quantities which have no dimensions but have variable values, are called dimensional variables., Eg:- angle, strain, sin θ, cos θ etc., 3. DIMENSIONAL CONSTANTS :The physical quantity which possess dimensions and have constant values, are called dimensional constant., Eg:- Plank’s constant, Gravitational constant etc.., 4. DIMENSIONLESS CONSTANTS :The quantities which do not have dimensions but have constant values are, called dimensionless constant., Eg:- π, e, pure number like 1, 2, 3 ... etc..
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13, Uses of dimensional analysis/formula, The dimensional analysis has the following uses., i), Conversion of one system of units into the other system of unit., ii), Checking the correctness of the given physical relation., iii), To derive the relationship between various physical quantities., CONVERSION OF ONE SYSTEM OF UNITS TO ANOTHER SYSTEM OF UNITS, A physical quantity (X) can be written as, X = nu, where n is the numerical value of the quantity X and u is its unit expressed in terms, of mass length and time., Let M1, L1, T1 be the fundamental units of the physical quantity X in one system., Let n1 be the numerical value of the physical quantity in the first system. a, b, and c, are the dimensions of mass, length and time respectively., Therefore, physical quantity in the first system can be written as, X =n1[Ma1Lb1Tc1] -------------------------(1), Let M2, L2, T2 be the fundamental units of the physical quantity X in the second, system and n2 be its numerical value., Therefore,, X =n2[Ma2Lb2Tc2] -------------------------(2), From equations (1) and (2), we have, n2[Ma2Lb2Tc2] = n1[Ma1Lb 1Tc 1], , Using eqn. (3), the numerical value of a physical quantity in the second system of, unit can be calculated if its numerical value in the first system of unit is known.
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14, , CHECKING THE CORRECTNESS OF THE GIVEN PHYSICAL RELATION, To check the correctness of the given physical relation among various physical, quantities, the followings steps are followed., Write the dimensional formulae of all physical quantities, in the given relation/formula, Write the dimensional formulae in the sequence below, the given physical quantities in the given, relation/formula, Apply the principle of homogeneity, If dimensions of the fundamental quantities (M, L and, T) of both sides of the formula are same, then the given, formula is dimensionally correct., If dimensions of the fundamental quantities (M, L and, T) of both sides of the formula are not same, then the, given formula is not dimensionally correct., Q. CHECK THE DIMENSIONAL CONSISTENCY OF THE FOLLOWING RELATION:, -----------------------(i), Here, F= force; S=distance; m = mass; u = initial velocity; v= final velocity., Solution, the relation will be dimensionally consistent if the dimensions of each, term are the same., Dimensions of ‘F’ = [MLT-2] ; Dimensions of ‘S’ = [L], Dimensions of ‘u’ or ‘v’= [LT-1] ; Dimensions of ‘m’ = [M], Since the constant ½ has no dimensions, it will not enter into the dimensional, equation., Putting the dimensions of various physical quantities in eq. (i), we have,, [MLT-2] [L] = [M] [LT-1]-2 -[M] [LT-1]2, Or, [ML2T-2] =[ML2T-2] - [ML2T-2], Or, [ML2T-2] = *[ML2T-2], Hence, the given relation is dimensionally correct., TO DERIVE THE RELATIONSHIP BETWEEN VARIOUS PHYSICAL, QUANTITIES:Using the same principle of homogeneity of dimensions, we can derive the, formula of a physical quantity, provided we know the factors on which the physical, quantity depends., Q. Derive an expression for time period (t) of a simple pendulum, which may depend, on mass of bob (m), length of pendulum (l) and acceleration due to gravity (g)., Let t α malbgc., Where a, b, c are the dimensions., t = k malbgc -----(1), where k is the a dimensionless constant of proportionality.
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15, , Writing the dimensions in terms of M, L, T on either side,, [M0L0T1], = [Ma] [Lb] [LT-2], = MaLbLcT-2, = MaLbLcT-2, = [MaLb+cT-2c]-----------------(2), Applying the principle of homogeneity of dimensions, we get, a=0, b+c=0 --------------- (3), -2c=1, => c = ½, eqn. (3) becomes,, b = -c, => b = -(-½), Therefore, b = ½, Putting the values of a, b, c in ..., t = km0 l½g-½, t=k, Using other methods, we calculate the value of dimensionless constant., k = 2π, therefore, t = 2π, SIGNIFICANT FIGURES :The digits that are known reliably plus the first uncertain digit are known as, significant figures., Eg:- 1) if length = 375.5 m, It has four significant figures 3, 7, 4 and 5., The digits 3, 7 and 4 are certain and reliable while the digit 5 is uncertain., 2. t= 1.37 second, It has 3 significant figures 1, 3 & 7. The digits 1 and 3 are certain and reliable while, the digit 7 is uncertain., RULES FOR SIGNIFICANT FIGURES :1. All Non-zero digits are always significant figures:Examples :, NUMBER, SIGNIFICANT FIGURES, 17, 2, 178, 3, 1782, 4, 17825, 5, 2. All zeros occurring between non-zero digits are significant figures:Examples :, NUMBER, SIGNIFICANT FIGURES, 401, 3, 4012, 4, 40056, 5, 400006, 6
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16, , 3. All zeros to the right of the last non-zero digit are not significant figures:Examples :, NUMBER, SIGNIFICANT FIGURES, 20, 1, 210, 2, 2130, 3, 20350, 4, 4. All zero to the right of a decimal point and to the left of a non-zero digit, are not significant figures : Examples :, NUMBER, SIGNIFICANT FIGURES, 0.04, 1, 0.004, 1, 0.0045, 2, 0.0456, 3, 0.0004564, 4, 5. All zeroes to the right of a decimal point and to the right of a non-zero, digit are significant figures:Examples :, NUMBER, SIGNIFICANT FIGURES, 0.20, 2, 0.230, 3, 0.2370, 4, ., Question:
