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Physics Notes (Class https://tapoj.com PHYSICS NOTES (CLASS- XI) FOR CLASS 11 ONLINE CLASSES CONTACT US AT - [email protected] or WhatsApp-7254930990 1 https://tapoj.com (Class-XI) CHAPTER -2 UNITS & MEASUREMENT CONTENTS SL NO TOPIC PAGE NO 1. INTRODUCTION 3 2. THE INTERNATIONAL SYSTEM OF UNITS 4 3. MEASUREMENT OF LENGTH 5 4. MEASUREMENT OF MASS 10 5. MEASUREMENT OF TIME 11 6 ACCURACY , PRECISION OF INSTRUMENTS AND 13 ERROERS IN MEASUREMENT 7. SIGNIFICANT FIGURES 18 8 DIMENSIONS OF PHYSICAL QUANTITIES 22 9. DIMENSIONAL FORMULAE AND DIMESIONAL 23 EQUATIONS 10. DIMESNSIONAL ANALYSIS AND ITS APPLICATION 24 FOR CLASS 11 ONLINE CLASSES CONTACT US AT - [email protected] or WhatsApp-7254930990 2 https://tapoj.com INTRODUCTION Physics is a quantitative science, based on measurement of physical quantities. Certain physical quantities have been chosen as fundamental or base quantities (such as length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity). A physical quantity is completely specified if it has: Magnitude of a Physical Quantity = Numerical value *Unit There are also physical quantities which are not even completely specified even by magnitude, unit, and direction. These physical quantities are called Tensors. Example- Moment Of Inertia DEFINITIONS: UNIT: Each base quantity is defined in terms of a certain basic, arbitrarily chosen but properly standardised reference standard called unit (such as metre, kilogram, second, ampere, kelvin, mole and candela). FUNDAMENTAL OR BASE UNIT: The units for the fundamental or base quantities are called fundamental or base units. Example-meter, hour etc. FOR CLASS 11 ONLINE CLASSES CONTACT US AT - [email protected] or WhatsApp-7254930990 3 https://tapoj.com DERIVED UNITS: Other physical quantities, derived from the base quantities, can be expressed as a combination of the base units and are called derived units. Example- Newton, Watt etc. SYSTEM OF UNITS: A complete set of units, both fundamental and derived, is called a system of units. Example- CGS system, MKS system, FPS system. INTERNATIONAL SYSTEM OF UNITS: The measurement system used at present is Système Internationale d’ Unites (French for International System of Units), abbreviated as SI. The International System of Units (SI) based on seven base units is at present internationally accepted unit system and is widely used throughout the world. The SI units are used in all physical measurements, for both the base quantities and the derived quantities obtained from them. Certain derived units are expressed by means of SI units with special names (such as joule, newton, watt, etc.). The SI units have well defined and internationally accepted unit symbols (such as m for metre, kg for kilogram, s for second, A for ampere, N for newton etc.) There are seven Basic Units: Length, Mass, Time, Electric Current, Temperature, Amount of Substance, and Luminous Intensity. Besides the seven base units, there are two more units that are defined for : (a) Plane angle “d θ “as the ratio of length of arc ds to the radius r (dθ =ds/dr) & (b) Solid angle “dΩ” as the ratio of the intercepted area dA of the spherical surface, described about the apex O as the centre, to the square of its radius r (dΩ=dA/풓ퟐ) FOR CLASS 11 ONLINE CLASSES CONTACT US AT - [email protected] or WhatsApp-7254930990 4 https://tapoj.com The unit for plane angle is radian with the symbol rad and the unit for the solid angle is steradian with the symbol sr. Both these are dimensionless quantities. Seven Fundamental Units and Their Definition: MEASUREMENT OF LENGTH We already know some direct methods of measuring length such as ruler, Vernier callipers etc. A metre scale is used for lengths from 10-3 m to 102 m. A Vernier callipers is used for lengths to an accuracy of 10-4 m. A screw gauge and a spherometer can be used to measure lengths as less as to 10-5 m. To measure lengths beyond these ranges, we make use of some special indirect methods. FOR CLASS 11 ONLINE CLASSES CONTACT US AT - [email protected] or WhatsApp-7254930990 5 https://tapoj.com Measurement Of Large Distance : The method we use for measuring large distances such as distance of stars from earth is called Parallax Method. What is Parallax? Parallax is the effect whereby the position or direction of an object appears to differ when viewed from different positions. Example: When we hold a pencil against some specific point on the background, and look through one of our left eye (closing right eye) and again through our right eye, we notice that the positions of pencils with respect to the background are different. This is called Parallax and the distance between the two points of observation is called Basis. To measure the distance D of a faraway planet S by the parallax method, it is observed from two different positions (observatories) A and B on the Earth, separated by distance AB = b at the same time as shown in Fig. 2.2 Parallactic Angle : It is the angle made between the great circle passing through between the celestial object and zenith, and the hour of object. The ∠ASB in Fig. 2.2 represented by symbol θ is called the parallax angle or parallactic angle. As the planet is very far away, b/D<< 1, and therefore, θ is very small By approximation: AB as an arc of length b of a circle with centre at S and the distance D as the radius AS = BS AB = b = D θ where θ is in radians. D= b/ θ FOR CLASS 11 ONLINE CLASSES CONTACT US AT - [email protected] or WhatsApp-7254930990 6 https://tapoj.com If d is the diameter of the planet and α the angular size of the planet (the angle subtended by d at the earth), then α = d/D α (Angular Size of Planet)= the angle between the two directions when two diametrically opposite points of the planet are viewed through the telescope & d = Diameter of the planet EXAMPLES: 1. Calculate the angle of (a) 10 (degree) (b) 1′ (minute of arc or arcmin) and (c) 1″ (second of arc or arc second) in radians. Use 3600=2π rad, 10=60′ and 1′ = 60 ″. Ans: (a) We have 3600 = 2π rad, 10= (π /180) rad = 1.745×10−2rad (b) 10= 60′ = 1.745×10–2 rad, 1′ = 2.908×10−4 rad~ 2.91×10−4rad (c) 1′ = 60″ = 2.908×10–4 rad, 1″ = 4.847× 10−4rad ~ 4.85× 10−4rad 2. A man wishes to estimate the distance of a nearby tower from him. He stands at a point A in front of the tower C and spots a very distant object O in line with AC. He then walks perpendicular to AC up to B, a distance of 100 m, and looks at O and C again. Since O is very distant, the direction BO is practically the same as AO; but he finds the line of sight of C shifted from the original line of sight by an angle θ =400 (θ is known as ‘parallax’) estimate the distance of the tower C from his original position A. Ans: We have, parallax angle θ = 400 AB = AC tan θ AC = AB/tanθ = 100 m/tan400 =100 m/0.8391 = 119 m FOR CLASS 11 ONLINE CLASSES CONTACT US AT - [email protected] or WhatsApp-7254930990 7 https://tapoj.com 3. The moon is observed from two diametrically opposite points A and B on Earth. The angle θ subtended at the moon by the two directions of observation is 10 54′. Given the diameter of the Earth to be about 1.276 × 10−7 m, compute the distance of the moon from the Earth. Ans: We have θ = 1° 54′ = 114′ = (114*60)”*(4.85*10−6 ) rad = 3.32*10−2 rad Since, 1”=4.8510−6 rad Also b= AB=1.276*107 m Hence, D=b/ θ= (1.276*107 /3.32*10−2 ) = 3.84*108 Estimation of Very Small Distances: Size of a Molecule To measure a very small size, like that of a molecule (10−8 m to10−9 m), Electron Microscopes are used. These are controlled by electric and magnetic fields. Electron microscopes have a resolution of 0.6 Å . They can almost resolve atoms and molecules in a material. In recent times, tunnelling microscopy has been developed in which again the limit of resolution is better than an angstrom. It is possible to estimate the sizes of molecules. Estimating Size of Oleic Acid: Oleic acid is a soapy liquid with large molecular size of the order of10−9 m. The idea is to first form mono-molecular layer of oleic acid on water surface. 1 푐푚3 of oleic acid in alcohol is dissolved to make a solution of 20 cm3. 1푐푚3 of this solution is taken and diluted to 20 cm3, using alcohol. So, the concentration of the solution is equal to 1/(20*20*20)cm3 of oleic acid/cm3 of solution. FOR CLASS 11 ONLINE CLASSES CONTACT US AT - [email protected] or WhatsApp-7254930990 8 https://tapoj.com Some lycopodium powder is sprinkled on the surface of water in a large trough and one drop of this solution s put in the water. The oleic acid drop spreads into a thin, large and roughly circular film of molecular thickness on water surface. The diameter of the thin film is measured quickly to get its area A. Suppose we have dropped n drops in the water. Initially, we determine the approximate volume of each drop (V cm3). Volume of n drops of solution = nV cm3 Amount of oleic acid in this solution = nV(1/(20*20))cm3 This solution of oleic acid spreads very fast on the surface of water and forms a very thin layer of thickness t Thickness = (Volume of the film/Area of the film) t = nV/(20*20) cm If we assume that the film has mono-molecular thickness, then this becomes the size or diameter of a molecule of oleic acid.
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