Physics Class 9th PDF

Unit 1 Physical Quantities and Measurement STUDENT’S LEARNING OUTCOMES After studying this unit, the students will be able to: describe the crucial role of Physics in Science, Technology and Society. explain with examples that Science is based on physical quan...

Unit 1 Physical Quantities and Measurement STUDENT’S LEARNING OUTCOMES After studying this unit, the students will be able to: describe the crucial role of Physics in Science, Technology and Society. explain with examples that Science is based on physical quantities which consist of numerical magnitude and a unit. differentiate between base and derived physical quantities. list the seven units of System International (SI) alongwith their symbols and physical quantities (standard definitions of SI units are not required). interconvert the prefixes and their symbols to indicate multiples and sub-multiples for both base and derived units. write the answer in scientific notation in measurements and calculations. describe the working of Vernier Callipers and screw gauge for measuring length. Conceptual linkage. identify and explain the limitations of measuring This unit is built on instruments such as metre rule, Vernier Callipers Measurement and screw gauge. -Science-VIII Scientific Notation describe the need using significant figures for -Maths-IX recording and stating results in the laboratory. This unit leads to: Measurement -Physics-XI Physics IX 2 Unit 1: Physical Quantities and Measurement Major Concepts INVESTIGATION SKILLS 1.1 Introduction to Physics The students will be able to: 1.2 Physical quantities compare the least count/ accuracy of the following 1.3 International System of measuring instruments and state their measuring units range: 1.4 Prefixes (multiples and (i) Measuring tape sub-multiples) 1.5 Scientific notation/ (ii) Metre rule Standard form (iii) Vernier Callipers 1.6 Measuring instruments metre rule (iv) Micrometer screw gauge Vernier Callipers make a paper scale of given least count e.g. 0.2 cm screw gauge and 0.5 cm. physical balance determine the area of cross section of a solid cylinder stopwatch with Vernier Callipers and screw gauge and evaluate measuring cylinder which measurement is more precise. 1.7 An introduction to significant figures determine an interval of time using stopwatch. determine the mass of an object by using different types of balances and identify the most accurate balance. When you can measure what you are speaking about and determine volume of an irregular shaped object using express it in numbers, you a measuring cylinder. know something about it. When you cannot measure what you List safety equipments and rules. are speaking about or you Use appropriate safety equipments in laboratory. cannot express it in numbers, your knowledge is of a meagre SCIENCE, TECHNOLOGY AND SOCIETY and of unsatisfactory kind. CONNECTION The students will be able to: determine length, mass, time and volume in daily life Lord Kelvin activities using various measuring instruments. FOR YOUR INFORMATION list with brief description the various branches of physics. Man has always been inspired by the wonders of nature. He has always been curious to know the secrets of nature and remained in search of the truth and reality. He observes various phenomena and tries to find their answers by logical reasoning. The knowledge gained through observations and Andromeda is one of the billions of galaxies of known universe. Physics IX 3 Unit 1: Physical Quantities and Measurement experimentations is called Science. The word science is derived from the Latin word scientia, which means knowledge. Not until eighteenth century, various aspect of material objects were studied under a single subject called natural philosophy. But as the knowledge increased, it was divided into two main streams; Physical sciences — which deal with the study of non-living things and Biological sciences — which are concerned with the BRANCHES OF PHYSICS study of living things. Mechanics: It is the study of motion of objects, Measurements are not confined to science. its causes and effects. They are part of our lives. They play an important role to Heat: It deals with the nature of heat, describe and understand the physical world. Over the modes of transfer and effects of centuries, man has improved the methods of heat. measurements. In this unit, we will study some of Sound: It deals with the physical aspects physical quantities and a few useful measuring of sound waves, their production, instruments. We will also learn the measuring techniques properties and applications. that enable us to measure various quantities accurately. Light (Optics): It is the study of physical aspects of light, its properties, working 1.1 INTRODUCTION TO PHYSICS and use of optical instruments. In the nineteenth century, physical sciences Electricity and Magnetism: It is the study of the charges at were divided into five distinct disciplines; physics, rest and in motion, their effects chemistry, astronomy, geology and meteorology. The and their relationship with magnetism. most fundamental of these is the Physics. In Physics, we Atomic Physics: study matter, energy and their interaction. The laws and It is the study of the structure and principles of Physics help us to understand nature. properties of atoms. Nuclear Physics: The rapid progress in science during the recent It deals with the properties and years has become possible due to the discoveries and behaviour of nuclei and the particles within the nuclei. inventions in the field of Physics. The technologies are Plasma Physics: the applications of scientific principles. Most of the It is the study of production, technologies of our modern society throughout the world properties of the ionic state of matter - the fourth state of matter. are related to Physics. For example, a car is made on the Geophysics: principles of mechanics and a refrigerator is based on the It is the study of the internal principles of thermodynamics. structure of the Earth. In our daily life, we hardly find a device where Physics is not involved. Consider pulleys that make it easy to lift heavy loads. Electricity is used not only to Physics IX 4 Unit 1: Physical Quantities and Measurement get light and heat but also mechanical energy that drives fans and electric motors etc. Consider the means of transportation such as car and aeroplanes; domestic appliances such as air- conditioners, refrigerators, vacuum-cleaners, washing machines, and microwave ovens etc. Similarly the means of communication such as radio, TV, telephone and computer are the result of applications of Physics. These devices have (a) (b) made our lives much easier, faster and more comfortable than Figure 1.1 (a) a vacuum cleaner the past. For example, think of what a mobile phone smaller (b) a mobile phone than our palm can do? It allows us to contact people anywhere in the world and to get latest worldwide information. We can DO YOU KNOW? take and save pictures, send and receive messages of our friends. We can also receive radio transmission and can use it as a calculator as well. However, the scientific inventions have also caused harms and destruction of serious nature. One of which is the environmental pollution and the other is the deadly weapons. QUICK QUIZ 1. Why do we study physics? 2. Name any five branches of physics. Wind turbines are used to produce pollution free electricity. 1.2 PHYSICAL QUANTITIES All measurable quantities are called physical quantities such as length, mass, time and temperature. A physical quantity possesses at least two characteristics in common. One is its numerical magnitude and the other is the unit in which it is measured. For example, if the length of a student is 104 cm then 104 is its numerical magnitude and centimetre is the unit of measurement. Similarly when a grocer says that each bag contains 5 kg sugar, he is describing its numerical magnitude as well as the unit of measurement. It would be meaningless to state 5 or kg only. Physical quantities are divided into base quantities and derived quantities. Figure 1.2: Measuring height. Physics IX 5 Unit 1: Physical Quantities and Measurement BASE QUANTITIES There are seven physical quantities which Base quantities are the form the foundation for other physical quantities. quantities on the basis of These physical quantities are called the base which other quantities are quantities. These are length, mass, time, electric expressed. current, temperature, intensity of light and the amount of a substance. DERIVED QUANTITIES Those physical quantities which are expressed The quantities that are in terms of base quantities are called the derived expressed in terms of base quantities. These include area, volume, speed, force, quantities are called derived work, energy, power, electric charge, electric quantities. potential, etc. 1.3 INTERNATIONAL SYSTEM OF UNITS Measuring is not simply counting. For example, if we need milk or sugar, we must also understand how much quantity of milk or sugar we are talking about. Thus, there is a need of some standard quantities for measuring/comparing unknown quantities. Once a standard is set for a quantity then it can be expressed in terms of that standard quantity. This standard quantity is called a unit. Volume: 1 cm3 With the developments in the field of science 1 mL and technology, the need for a commonly acceptable system of units was seriously felt all over the world particularly to exchange scientific and technical information. The eleventh General Conference on 1 cm 10 cm = 1 dm Weight and Measures held in Paris in 1960 adopted a world-wide system of measurements called Volume is a derived quantity International System of Units. The International 1L = 1000 mL System of Units is commonly referred as SI. 1L = 1 dm3 = (10 cm)3 BASE UNITS = 1000 cm3 The units that describe base quantities are 1 mL = 1 cm3 called base units. Each base quantity has its SI unit. Express 1m3 in litres.......... L Physics IX 6 Unit 1: Physical Quantities and Measurement Table 1.1 shows seven base quantities, their SI units and their symbols. Table 1.1: Base quantities, their SI units with symbols DERIVED UNITS The units used to measure derived quantities are called derived units. Derived units are defined in terms of base units and are obtained by multiplying or dividing one or more base units with each other. The unit of area (metre)2 and the unit of volume (metre)3 are based on the unit of length, which is metre. Thus the unit of length is the base unit while the unit of area and volume are derived units. Speed is defined as distance covered in unit time; therefore its unit is metre per second. In the same way the unit of density, force, pressure, power etc. can be derived using one or more base units. Some derived units and their symbols are given in the Table 1.2. Table 1.2: Derived quantities and their SI units with symbols  Physics IX 7 Unit 1: Physical Quantities and Measurement QUICK QUIZ 1. How can you differentiate between base and derived quantities? 2. Identify the base quantity in the following: (i) Speed (ii) Area (iii) Force (iv) Distance 3. Identify the following as base or derived quantity: Table 1.3: Some Prefixes density, force, mass, speed, time, length, temperature and volume. 1.4 PREFIXES Some of the quantities are either very large or very small. For example, 250 000 m, 0.002 W and 0.000 002 g, etc. SI units have the advantage that their multiples and sub-multiples can be expressed in terms of prefixes. Prefixes are the words or letters added before SI units such as kilo, mega, giga and milli. These prefixes are given in Table 1.3. The prefixes are useful to express very large or small quantities. For example, divide 20,000 g by 1000 to express it into kilogramme, since kilo represents 103 or 1000. Thus or Table 1.4 shows some multiples and sub- multiples of length. However, double prefixes are not used. For example, no prefix is used with kilogramme since it already contains the prefix kilo. Prefixes given in Table 1.3 are used with both types base and derived Table 1.4: Multiples and sub-multiples of length units. Let us consider few more examples: (I) 200 000 ms-1 = 200x103 ms-1 =200kms-1 (ii) 4 800 000 W = 4 800x103W =4 800 kW = 4.8x106W =4.8 MW (iii) 3 300 000 000 Hz = 3 300x106 Hz =3300 MHz Physics IX 8 Unit 1: Physical Quantities and Measurement = 3.3x103 MHZ = 3.3 Ghz -3 (iv) 0.00002 g = 0.02x10 g = 20x10-6g Tidbits = 20 ug Mass of various objects (v) 0.000 000 0081m = 0.0081 x10-6m =8.1x10-9m 24 = 8.1 nm 10 g 22 10 g Earth’s atmosphere 1.5 SCIENTIFIC NOTATION to 2500 km A simple but scientific way to write large or small 1018g numbers is to express them in some power of ten. 1015g The Moon is 384000000 metres away from the Earth. Distance of the moon from the Earth can also be 1012g Ocean expressed as 3.84 x108 m. This form of expressing a 9 10 g number is called the standard form or scientific Elephant notation. This saves writing down or interpreting large 106g Average human numbers of zeros. Thus 3 10 g 1.0 litre of water In scientific notation a number is expressed as 0 10 g some power of ten multiplied by a number between 1 and 10. 10-3g -6 For example, a number 62750 can be 10 g expressed as 62.75x103 or 6.275x104 or 0.6275x105. All Grain of table salt -9 10 g these are correct. But the number that has one non-zero digit before the decimal i.e. 6.275x104 preferably be 10-12g taken as the standard form. Similarly the standard form of 10-15g 0.00045 s is 4.5x10-4s. -18 10 g Typical protein molecule -22 1. Name five prefixes most commonly used. 10 g Uranium atom 2. The Sun is one hundred and fifty million kilometres away Water molecules from the Earth. Write this 10-24g (a) as an ordinary whole number. (b) in scientific notation. 3. Write the numbers given below in scientific notation. -1 (a) 3000000000 ms (b) 6400000 m (c) 0.0000000016 g (d) 0.0000548 s  Physics IX 9 Unit 1: Physical Quantities and Measurement 1.6 MEASURING INSTRUMENTS FOR YOUR INFORMATION Measuring instruments are used to measure various physical quantities such as length, mass, time, volume, etc. Measuring instruments used in the past were not so reliable and accurate as we use today. For example, sundial, water clock and other time measuring devices used around 1300 AD were quite crude. On the other hand, digital clocks and watches used now-a-days are highly reliable and accurate. Hubble Space Telescope orbits Here we shall describe some measuring instruments around the Earth. It provides used in Physics laboratory. information about stars. THE METRE RULE 0 10 90 80 70 60 50 40 30 20 10 0 cm Figure 1.3: A metre rule (a) A metre rule is a length measuring instrument as shown in figure 1.3. It is commonly used in the 0 1 2 3 laboratories to measure length of an object or distance between two points. It is one metre long which is equal to (b) 100 centimetres. Each centimetre (cm) is divided into 10 0 1 2 3 small divisions called millimetre (mm). Thus one millimetre is the smallest reading that can be taken using Figure 1.4: Wrong position of the a metre rule and is called its least count. eye to note the reading. (b) Correct position of the eye to While measuring length, or distance, eye must be note the reading from a metre rule. kept vertically above the reading point as shown in figure 1.4(b). The reading becomes doubtful if the eye is positioned either left or right to the reading point. THE MEASURING TAPE Measuring tapes are used to measure length in metres and centimetres. Figure 1.5 shows a measuring tape used by blacksmith and carpenters. A measuring tape consists of a thin and long strip of cotton, metal or plastic generally 10 m, 20 m, 50 m or 100 m long. Figure 1.5: A measuring tape Measuring tapes are marked in centimetres as well as in inches. Physics IX 10 Unit 1: Physical Quantities and Measurement VERNIER CALLIPERS The accuracy obtained in measurements using a metre rule is upto 1 mm. However an accuracy greater than 1 mm can be obtained by using some Mini Exercise Cut a strip of paper sheet. MOVEABLE JAWS 0 1 2 3 4 5 6 7 8 9 10 11 12 cm FIX JAWS Fold it along its length. Now m mark centimetres and half 0 5 10 centimetre along its length Vernier Scale Main Scale using a ruler. Answer the Outer jaws following questions: Figure 1.6: A Vernier Callipers with jaws closed 1. What is the range of your other instruments such as a Vernier Callipers. A Vernier paper scale? Callipers consists of two jaws as shown in figure 1.6. One 2. What is its least count? is a fixed jaw with main scale attached to it. Main scale 3. Measure the length of a has centimetre and millimetre marks on it. The other jaw pencil using your paper is a moveable jaw. It has vernier scale having 10 divisions scale and with a metre over it such that each of its division is 0.9 mm. The ruler. Which one is more difference between one small division on main scale accurate and why? division and one vernier scale division is 0.1 mm. It is called least count (LC) of the Vernier Callipers. Least count of the Vernier Callipers can also be found as given below: Hence Working of a Vernier Callipers First of all find the error, if any, in the measuring instrument. It is called the zero error of the instrument. Knowing the zero error, necessary correction can be made to find the correct measurement. Such a correction is called zero correction of the instrument. Zero correction is the negative of zero error.  Physics IX 11 Unit 1: Physical Quantities and Measurement Zero Error and Zero Correction There is no zero error as zero line of vernier scale is coinciding with To find the zero error, close the jaws of Vernier the zero of main scale. Callipers gently. If zero line of the vernier scale coincides with the zero of the main scale then the zero error is zero MOVEABLE JAWS (figure 1.7a). Zero error will exist if zero line of the vernier 0 1 2 scale is not coinciding with the zero of main scale (figure 1.7b). Zero error will be positive if zero line of 0 5 10 vernier scale is on the right side of the zero of the main (a) scale and will be negative if zero line of vernier scale is on Zero error is (0+0.07) cm as 7th line the left side of zero of the main scale (figure 1.7c). of vernier scale is coinciding with one of the main scale division. Taking a Reading on Vernier Callipers MOVEABLE JAWS Let us find the diameter of a solid cylinder using 0 1 2 Vernier Callipers. Place the solid cylinder between jaws 0 5 10 of the Vernier Callipers as shown in figure 1.8. Close the Zero error is positive as zero line of jaws till they press the opposite sides of the object gently. vernier scale is on the right side of the zero of the main scale. (b) Zero error is (-0.1+0.08) cm as 8th line of vernier scale is coinciding 0 1 2 3 4 5 6 7 8 9 10 11 12 with main scale. cm FIX JAWS m 0 5 10 MOVEABLE JAWS 0 1 2 0 5 10 Figure 1.8: A cylinder placed between the outer jaws of Vernier Callipers. Zero error is negative as zero Note the complete divisions of main scale past line of the vernier scale is on the left side of the main scale. the vernier scale zero in a tabular form. Next find ( ) thevernier scale division that is coinciding with any Figure 1.7: Zero Error division on the main scale. Multiply it by least count of (a) zero (b) +0.07 cm Vernier Callipers and add it in the main scale reading. © cm. -0.02 This is equal to the diameter of the solid cylinder. Add zero correction (Z.C) to get correct measurement. Repeat the above procedure and record at least three observations with the solid cylinder displaced or rotated each time. Physics IX 12 Unit 1: Physical Quantities and Measurement QUICK QUIZ 1. What is the least count of the Vernier Callipers? 2. What is the range of the Vernier Callipers used in your Physics laboratory? DIGITAL VERNIER 3. How many divisions are there on its vernier scale? CALLIPERS 4. Why do we use zero correction? EXAMPLE 1.1 Find the diameter of a cylinder placed between the outer jaws of Vernier Callipers as shown in figure 1.8. SOLUTION Zero correction On closing the jaws of Vernier Callipers, the position of vernier scale as shown in figure 1.7(b). Main scale reading = 0.0 cm Vernier division coinciding with main scale = 7 div. Vernier scale reading = 7 x 0.01 cm = 0.07 cm Zero error =0.0 cm+0.07 cm Digital Vernier Callipers = +0.07 cm has greater precision than m e c h a n i c a l Ve r n i e r zero correction (Z.C) = - 0.07 cm Callipers. Least count of Diameter of the cylinder Digital Vernier Callipers is Main scale reading = 2.2 cm 0.01 mm. (when the given cylinder is kept between the jaws of the Vernier Callipers as shown in figure 1.8). Vernier div. coinciding with main scale div. = 6 div. Vernier scale reading = 6 x 0.01 cm = 0.06 cm Observed diameter of the cylinder = 2.2 cm+0.06 cm = 2.26 cm Correct diameter of the cylinder = 2.26cm0.07 cm = 2.19 cm Thus, the correct diameter of the given cylinder as found by Vernier Callipers is 2.19 cm.  Physics IX 13 Unit 1: Physical Quantities and Measurement SCREW GAUGE Tidbits A screw gauge is an instrument that is used to Relative sizes of molecules measure small lengths with accuracy greater than a and micro-organisms Vernier Calliper. It is also called as micrometer screw gauge. A simple screw gauge consists of a U-shaped 1A metal frame with a metal stud at its one end as shown in Molecule figure 1.9. A hollow cylinder (or sleeve) has a millimetre Small 1nm scale over it along a line called index line parallel to its Nanotechnology Relative sizes of cells and their components axis. The hollow cylinder acts as a nut. It is fixed at the 10nm end of U-shaped frame opposite to the stud. A Thimble has a threaded spindle inside it. As the thimble completes Electron microscope Virus one rotation, the spindle moves 1 mm along the index line. 100nm It is because the distance between consecutive threads on the spindle is 1 mm. This distance is called the pitch of Bacterium screw on the spindle. 1m Light microscope Animal 10m Ratchet Cell Stud Spindle Lock Main scale Circular scale 80 75 0 5 70 Plant 100m Cell 65 60 Hollow Thimble cylinder Index or sleeve 1mm line Metal frame Figure 1.9: A micrometer screw gauge 1 The thimble has 100 divisions around its one end. It is the circular scale of the screw gauge. As thimble completes one rotation, 100 divisions pass the index line and the thimble moves 1 mm along the main scale. Thus each division of circular scale crossing the index line moves the thimble through 1/100 mm or 0.01 mm on the main scale. Least count of a screw gauge can also be found as given below: Physics IX 14 Unit 1: Physical Quantities and Measurement As zero of circular scale is exactly on the index line hence there is no zero error. = 0.01 mm = 0.001 cm 10 Thus least count of the screw gauge is 0.01 mm 5 or 0.001 cm. 0 0 WORKING OF A SCREW GAUGE 95 The first step is to find the zero error of the screw 90 gauge. (a) ZERO ERROR Zero error is positive if zero of To find the zero error, close the gap between the circular scale has not reached zero of main scale. Here zero spindle and the stud of the screw gauge by rotating the error is +0.18 mm as 18th division on circular scale is before the ratchet in the clockwise direction. If zero of circular scale index line. coincides with the index line, then the zero error will be 30 zero as shown in figure 1.10(a). 25 Zero error will be positive if zero of circular scale 0 20 is behind the index line. In this case, multiply the number 15 of divisions of the circular scale that has not crossed the index line with the least count of screw gauge to find zero 10 5 error as shown in figure 1.10(b). (b) Zero error will be negative if zero of circular scale Zero error is negative if zero of has crossed the index line. In this case, multiply the circular scale has passed zero of number of divisions of the circular scale that has crossed main scale. Here zero error is –0.05 mm as 5 divisions of circular the index line with the least count of screw gauge to find scale has crossed the index line. the negative zero error as shown in figure 1.10(c). 5 EXAMPLE 1.2 0 0 Find the diameter of a wire using a screw gauge. 95 90 SOLUTION 85 The diameter of a given wire can be found as follows: c Figure 1.10: Zero Error in a screw (i) Close the gap between the spindle and the gauge: (a) zero stud of the screw gauge by turning the ratchet (b) + 0.18 mm (c) -0.05 mm. in the clockwise direction. (ii) Note main scale as well as circular scale readings to find zero error and hence zero correction of the screw gauge.  Physics IX 15 Unit 1: Physical Quantities and Measurement (iii) Open the gap between stud and spindle of the screw Mini Exercise gauge by turning the ratchet in anti clockwise direction. Place the given wire in the gap as shown in 1. What is the least count of a screw gauge? figure 1.11. Turn the ratchet so that the object is pressed gently between the studs and the spindle. 2. What is the pitch of your laboratory screw gauge? 3. What is the range of your Circular scale reading is 85 div. multiply it by 0.01 mm. This is laboratory screw gauge? Wire placed between the gap equal to 0.85 mm. 4. Which one of the two 95 90 instruments is more 0 85 precise and why? 80 75 Main scale reading (leaving the fractional part) is 1 mm. Here main scale reading is 0 mm and 23rd division of circular scale Figure 1.11: Measuring the diameter of a wire is before the index line. Hence using micrometer screen gauge. zero error is (0+24×0.01) mm = 0.24 mm. (iv) Note main scale as well as circular scale 35 readings to find the diameter of the given 30 wire. 0 25 (v) Apply zero correction to get the correct 20 diameter of the wire. 15 (vi) Repeat steps iii, iv and v at different places of 10 the wire to obtain its average diameter. Zero correction Closing the gap of the screw gauge (figure 1.12). Main scale reading = 0 mm Circular scale reading mm = 24 x 0.01 Zero error of the screw gauge = 0 mm+0.24 mm USEFUL INFORMATION = + 0.24 mm Least count of ruler is 1 Zero correction Z.C. = -0.24 mm mm. It is 0.1 mm for Vernier Callipers and 0.01mm for Diameter of the wire (figure 1.11) micrometer screw gauge. Thus measurements taken Main scale reading = 1 mm by micrometer screw gauge (when the given wire is pressed by are the most precise than the other two. the stud and spindle of the screw gauge) Physics IX 16 Unit 1: Physical Quantities and Measurement No. of divisions on circular scale = 85 div. Circular scale reading = 85x0.01 mm = 0.85 mm Observed diameter of the given wire =1mm+0.85 mm = 1.85 mm Correct diameter of the given wire = 1.85 mm - 0.24 mm = 1.61 mm Thus diameter of the given wire is 1.61 mm. MASS MEASURING INSTRUMENTS Pots were used to measure grain in various part of the world in the ancient times. However, balances were also in use by Greeks and Romans. Beam balances such as shown in figure 1.13 are still in use at many places. In a beam balance, the unknown mass is placed in one pan. It is balanced by putting known masses in the other pan. Today people use many types of mechanical and electronic balances. You might have seen electronic balances in sweet and grocery shops. These are more precise than beam balances and are easy to handle. PHYSICAL BALANCE A physical balance is used in the laboratory to measure the mass of various objects by comparison. It consists of a beam resting at the centre on a fulcrum Stirrup Beam Balancing Screw Hook Pointer is at Mini Exercise Pillar zero. Beam 1. What is the function of Plumbline is balanced balancing screws in a physical balance? Pointer 2. On what pan we place Pan the object and why? Scale 10 5 0 5 10 Arrestment knob Leveling Screw Figure 1.14: A physical balance  Physics IX 17 Unit 1: Physical Quantities and Measurement as shown in the figure 1.14. The beam carries scale pans over the hooks on either side. Unknown mass is placed LABORATORY SAFETY on the left pan. Find some suitable standard masses that EQUIPMENT cause the pointer to remain at zero on raising the beam. as shown in the figure 1.14. The beam carries scale pans over the hooks on either side. Unknown mass is placed on the left pan. Find some suitable standard masses that cause the pointer to remain at zero on raising the beam. EXAMPLE 1.3 Find the mass of a small stone by a physical balance. SOLUTION Follow the steps to measure the mass of a given object. (i) Adjusting the levelling screws with the help of plumbline to level the platform of physical balance. (ii) Raise the beam gently by turning the arresting knob Fire extinguisher clockwise. Using balancing screws at the ends of its beam, bring the pointer at zero position. (iii) Turn the arresting knob to bring the beam back on its supports. Place the given object (stone) on its left pan. (iv) Place suitable standard masses from the weight box on the right pan. Raise the beam. Lower the beam if its pointer is not at zero. (v) Repeat adding or removing suitable standard masses in the right pan till the pointer rests at zero on raising the beam. (vi) Note the standard masses on the right pan. Their sum is the mass of the object on the left pan. LEVER BALANCE A lever balance such as shown in figure 1.15 consists of a system of levers. When lever is lifted placing 0 the object in one pan and standard masses on the other Figure 1.15: A lever balance pan, the pointer of the lever system moves. The pointer is brought to zero by varying standard masses. Physics IX 18 Unit 1: Physical Quantities and Measurement ELECTRONIC BALANCE Electronic balances such as shown in figure 1.16 Glass case come in various ranges; milligram ranges, gram ranges and kilogramme ranges. Before measuring the mass of a Pan body, it is switched ON and its reading is set to zero. Next place the object to be weighed. The reading on the balance gives you the mass of the body placed over it. The most Accurate Balance Screw The mass of one rupee coin is done using Figure 1.16: An electronic balance different balances as given below: USEFUL INFORMATION (a) Beam Balance Let the balance measures coin's mass = 3.2 g The precision of a balance in measuring mass of A sensitive beam balance may be able to detect a change an object is different for as small as of 0.1 g Or 100 mg. different balances. A sensitive balance cannot measure large (b) Physical Balance masses. Similarly, a balance Let the balance measures coin's mass = 3.24 g that measures large masses cannot be sensitive. Least count of the physical balance may be as small as Some digital balances 0.01 g or 10 mg. Therefore, its measurement would be measure even smaller more precise than a sensitive beam balance. difference of the order of 0.0001g or 0.1 mg. Such (c) Electronic Balance balances are considered the Let the balance measures coin's mass = 3.247 g most precise balance. Least count of an electronic balance is 0.001 g or 1 mg. Therefore, its measurement would be more precise than a sensitive physical balance. Thus electronic balance is the most sensitive balance in the above balances. STOPWATCH 29 30 1 A stopwatch is used to measure the time interval 28 2 26 27 57 58 59 60 31 13 14 15 1 2 32 33 3 4 of an event. There are two types of stopwatches; 25 56 12 3 34 5 24 54 55 11 10 9 8 7 6 5 4 35 36 6 mechanical and digital as shown in figure 1.17 and 1.18. 23 53 22 52 37 38 7 A mechanical stopwatch can measure a time interval up 8 21 51 50 40 39 9 to a minimum 0.1 second. Digital stopwatches commonly 20 49 41 10 19 48 47 43 42 11 used in laboratories can measure a time interval as small 18 46 45 44 12 17 16 15 14 13 as 1/100 second or 0.01 second. Figure 1.17: A mechanical stopwatch  Physics IX 19 Unit 1: Physical Quantities and Measurement How to use a Stopwatch A mechanical stopwatch has a knob that is used to wind the spring that powers the watch. It can also be used as a start-stop and reset button. The watch starts when the knob is pressed once. When pressed second time, it stops the watch while the third press brings the needle back to zero position. The digital stopwatch starts to indicate the time lapsed as the start/stop button is pressed. As soon as start/stop button is pressed again, it stops and Figure 1.18: A digital stopwatch indicates the time interval recorded by it between start and stop of an event. A reset button restores its initial zero setting. MEASURING CYLINDER LABORATORY SAFETY A measuring cylinder is a glass or transparent EQUIPMENTS plastic cylinder. It has a scale along its length that A school laboratory must indicates the volume in millilitre (mL) as shown in figure have safety equipments such as: 1.19. Measuring cylinders have different capacities Waste-disposal basket from 100 mL to 2500 mL. They are used to measure Fire extinguisher. the volume of a liquid or powdered substance. It is also Fire alarm. used to find the volume of an irregular shaped solid First Aid Box. insoluble in a liquid by displacement method. The solid Sand and water buckets. is lowered into a measuring cylinder containing Fire blanket to put off fire. Substances and equipments that need water/liquid. The level of water/liquid rises. The extra care must bear proper warning increase in the volume of water/liquid is the volume of signs such as given below: the given solid object. 200 ml 200 ml 180 180 160 160 140 140 120 120 100 100 80 80 60 60 40 40 20 20 (a) Incorrect position (a) Correct position 0 0 Figure 1.19(a) Wrong way to note the liquid level keeping eye above liquid level, (b) correct position of eye to note the liquid level keeping eye at liquid level. Physics IX 20 Unit 1: Physical Quantities and Measurement HOW TO USE A MEASURING CYLINDER LABORATORY SAFETY RULES While using a measuring cylinder, it must be kept The students should know what to vertical on a plane surface. Take a measuring cylinder. do in case of an accident. The Place it vertically on the table. Pour some water into it. charts or posters are to be Note that the surface of water is curved as shown in figure displayed in the laboratory to 1.19. The meniscus of the most liquids curve downwards handle situations arising from any while the meniscus of mercury curves upwards. The mishap or accident. For your own correct method to note the level of a liquid in the cylinder safety and for the safety of others in is to keep the eye at the same level as the meniscus of the the laboratory, follow safety rules liquid as shown in figure 1.19(b). It is incorrect to note the given below: liquid level keeping the eye above the level of liquid as shown in figure 1.19 (a). When the eye is above the liquid Do not carry out any experiment level, the meniscus appears higher on the scale. without the permission of your Similarly when the eye is below the liquid level, the teacher. meniscus appears lower than actual height of the liquid. Do not eat, drink, play or run in MEASURING VOLUME OF AN IRREGULAR SHAPED the laboratory. SOLID Read the instructions carefully Measuring cylinder can be used to find the to familiarize yourself with the volume of a small irregular shaped solid that sinks in possible hazards before water. Let us find the volume of a small stone. Take some handling equipments and water in a graduated measuring cylinder. Note the materials. volume Vi of water in the cylinder. Tie the solid with a Handle equipments and thread. Lower the solid into the cylinder till it is fully materials with care. immersed in water. Note the volume Vf of water and the Do not hesitate to consult your solid. Volume of the solid will be Vf - Vi. teacher in case of any doubt. Do not temper with the electrical 1.7 SIGNIFICANT FIGURES appliances and other fittings in The value of a physical quantity is expressed by a the laboratory. number followed by some suitable unit. Every Report any accident or injuries measurement of a quantity is an attempt to find its true immediately to your teacher. value. The accuracy in measuring a physical quantity depends upon various factors: + the quality of the measuring instrument + the skill of the observer + the number of observations made For example, a student measures the length of a book as 18 cm using a measuring tape. The numbers of significant figures in his/her measured  Physics IX 21 Unit 1: Physical Quantities and Measurement value are two. The left digit 1 is the accurately known digit. While the digit 8 is the doubtful digit for which the student may not be sure. Another student measures the same book using a ruler and claims its length to be 18.4 cm. In this case all the three figures are significant. The two left digits 1 and 8 are RULES TO FIND THE accurately known digits. Next digit 4 is the doubtful digit for SIGNIFICANT DIGITS IN A MEASUREMENT which the student may not be sure. A third student records the length of the book as (i) Digits other than zero are always significant. 18.425 cm. Interestingly, the measurement is made using the 27 has 2 significant digits. same ruler. The numbers of significant figures is again three; consisting of two accurately known digits 1, 8 and the first 275 has 3 significant digits. doubtful digit 4. The digits 2 and 5 are not significant. It is (ii) Zeros between because the reading of these last digits cannot be justified significant digits are also using a ruler. Measurement upto third or even second decimal significant. place is beyond the limit of the measuring instrument. 2705 has 4 significant digits. An improvement in the quality of measurement by (iii) Final zero or zeros after using better instrument increases the significant figures in the decimal are significant. measured result. The significant figures are all the digits that 275.00 has 5 significant are known accurately and the one estimated digit. More digits. significant figure means greater precision. The following rules (iv) Zeros used for spacing are helpful in identifying significant figure: the decimal point are not significant. Here zeros (i) Non-zero digits are always significant. are placeholders only. 0.03 has 1 significant digit. (ii) Zeros between two significant figures are 0.027 has 2 significant also significant. digits. (iii) Final or ending zeros on the right in EXAMPLE decimal fraction are significant. (iv) Zeros written on the left side of the decimal point for the purpose of spacing the decimal point are not significant. (v) In whole numbers that end in one or more zeros without a decimal point. These zeros may or may not be significant. In such cases, it is not clear which zeros serve to Physics IX 22 Unit 1: Physical Quantities and Measurement locate the position value and which are actually parts of the measurement. In such a case, express the quantity using scientific notation to find the significant zero. EXAMPLE 1.4 Find the number of significant figures in each of the following values. Also express them in scientific notations. a) 100.8 s b) 0.00580 km Rounding the Numbers (i) lf the last digit is less than c) 210.0 g 5 then it is simply dropped. This decreases the SOLUTION number of significant digits in the figure. (a) All the four digits are significant. The zeros between the two significant figures 1 and 8 are For example, significant. To write the quantity in scientific 1.943 is rounded to 1.94 notation, we move the decimal point two (3 significant figure) places to the left, thus (ii) If the last digit is greater than 5, then the digit on 100.8 s = 1.008 x102 s its left is increased by one. This also decreases (b) The first two zeros are not significant. They are the number of significant used to space the decimal point. The digit 5,8 and digits in the figure. the final zero are significant. Thus there are three For example, significant figures. In scientific notation, it can be 1.47 is rounded to two written as 5.80x10-3 km. significant digits 1.5 (c) The final zero is significant since it comes after (iii) If the last digit is 5, then the decimal point. The zero between last zero and it is rounded to get nearest even number. 1 is also significant because it comes between the significant figures. Thus the number of For example, significant figures in this case is four. In scientific 1.35 is rounded to 1.4 and notation, it can be written as 1.45 is also rounded to 1.4 210.0 g = 2.100 x 102g Physics IX 23 Unit 1: Physical Quantities and Measurement SUMMARY Physics is a branch of Science that deals with matter, energy and their The words or letters added before a relationship. unit and stand for the multiples orsub- multiples of that unit are known as Some main branches of Physics prefixes. For example, kilo, mega, are mechanics, heat, sound, light milli, micro, etc. (optics), electricity and magnetism, nuclear physics and quantum A way to express a given number as a physics. number between 1 and 10 multiplied Physics plays an important role in by 10 having an appropriate power is our daily life. For example, called scientific notation or standard electricity is widely used form. everywhere, domestic appliances, An instrument used to measure small office equipments, machines used lengths such as internal or external in industry, means of transport and diameter or length of a cylinder, etc is communication etc. work on the called as Vernier Callipers. basic laws and principles of Physics. A Screw gauge is used to measure small lengths such as diameter of a A measurable quantity is called a wire, thickness of a metal sheet, etc. physical quantity. Physical balance is a modified type of Base quantities are defined beam balance used to measure small independently. Seven quantities masses by comparison with greater are selected as base quantities. accuracy. These are length, time, mass, electric current, temperature, A stopwatch is used to measure the intensity of light and the amount of time interval of an event. Mechanical a substance. stopwatches have least count upto 0.1 seconds. Digital stopwatch of The quantities which are least count 0.01s are common. expressed in terms of base quantities are called derived A measuring cylinder is a graduated quantities. For example, speed, glass cylinder marked in millilitres. It area, density, force, pressure, is used to measure the volume of a energy, etc. liquid and also to find the volume of an irregular shaped solid object. A world-wide system of measurements is known as All the accurately known digits and international system of units (SI). In the first doubtful digit in an expression SI, the units of seven base are called significant figures. It quantities are metre, kilogramme, reflects the precision of a measured second, ampere, kelvin, candela value of a physical quantity. and mole. Physics IX 24 Unit 1: Physical Quantities and Measurement Encircle the correct answer from A student claimed the diameter the given choices. of a wire as 1.032 cm using The number of base units in SI Vernier Callipers. Upto what are: extent do you agree with it? (a) 3 (b)6 (c)7 (d)9 (a) 1 cm (b) 1.0 cm Which one of the following unit (c) 1.03 cm (d) 1.032 cm is not a derived unit? A measuring cylinder is used (a) pascal (b) kilogramme to measure: (c) newton (d) watt (a) mass (b) area Amount of a substance in terms (c) volume (d) level of a liquid of numbers is measured in: (a) gram (b) kilogramme A student noted the thickness (c) newton (d) mole of a glass sheet using a screw gauge. On the main scale, it An interval of 200u s is equivalent reads 3 divisions while 8th to division on the circular scale coincides with index line. Its (a) 0.2 s (b) 0.02 s thickness is: -4 (c) 2x10 s (d) 2x10-6s (a) 3.8 cm (b) 3.08 mm (c) 3.8 mm (d) 3.08 m Which one of the following is the smallest quantity? Significant figures in an (a) 0.01 g (b) 2 mg expression are : (a) all the digits (c) 100 u g (d) 5000 ng (b) all the accurately known digits Which instrument is most (c) all the accurately known digits suitable to measure the internal and the first doubtful digit diameter of a test tube? (d) all the accurately known and all (a) metre rule the doubtful digits (b) Vernier Callipers (c) measuring tap What is the difference between base (d) screw gauge quantities and derived quantities? Give three examples in each case. Physics IX 25 Unit 1: Physical Quantities and Measurement Pick out the base units in the Why is the use of zero error following: necessary in a measuring joule, newton, kilogramme, hertz, instrument? mole, ampere, metre, kelvin, coulomb and watt. What is a stopwatch? What is the least count of a mechanical Find the base quantities involved stopwatch you have used in the in each of the following derived laboratories? quantities: (a) speed (b) volume Why do we need to measure (c) force (d) work extremely small interval of times? Estimate your age in seconds. What role SI units have played in What is meant by significant the development of science? figures of a measurement? What is meant by vernier How is precision related to the constant? significant figures in a measured What do you understand by quantity? the zero error of a measuring instrument? PROBLEMS Express the following Rewrite the f ollowing i n quantities using prefixes. standard form. (a) 5000 g (a) 1168x10-27 (b) 32x10-5 (b) 2000 000 W (c) 725 x10-5 kg (d) 0.02 x10-8 -10 (b) 52 x10 kg {(a) 1.168x10-24 (b) 3.2x106 -8 (c) 225x10 s (c)7.25g (d) 2x10-10} {(a) 5 kg (b)2MW Write the following quantities in (c) 5.2 ug (d) 2.25 us } standard form. How do the prefixes micro, (a) 6400 km nano and pico relate to each (b) 380 000 km other? (c) 300 000 000 ms-1 Your hair grow at the rate of (d) seconds in a day 1 mm per day. Find their growth {(a) 6.4x103 km (b) 3.8x105 km rate in nm s-1. (11.57 nm s-1) (c) 3x108ms1 (d) 8.64x104s} Physics IX 26 Unit 1: Physical Quantities and Measurement 1.6 On closing the jaws of a Vernier (a) 3.0066 m (b) 0.00309 kg Callipers, zero of the vernier scale is on the right to its main scale such (c) 5.05x10-27 kg (d) 301.0 s that 4th division of its vernier scale {(b) and (c)} coincides with one of the main scale division. Find its zero error and zero 1.9 What are the significant figures in correction. the following measurements? (a) 1.009 m (b) 0.00450 kg (+0.04 cm, -0.04 cm) (c) 1.66x10-27 kg (d) 2001 s 1.7 A screw gauge has 50 divisions on {(a) 4 (b) 3 (c) 3 (d) 4} its circular scale. The pitch of the screw gauge is 0.5 mm. What is its 1.10 A chocolate wrapper is 6.7 cm least count? long and 5.4 cm wide. Calculate its area upto reasonable (0.001 cm) number of significant figures. 1.8 Which of the following quantities (36 cm2) have three significant figures?  Unit 2 Kinematics STUDENT’S LEARNING OUTCOMES After studying this unit, the students will be able to: describe using examples how objects can be at rest and in motion simultaneously. identify different types of motion i.e. translator/, (linear, random, and circular); rotatory and vibratory motions and distinguish among them. differentiate with examples between distance and displacement, speed and velocity. differentiate with examples between scalar and vector quantities. represent vector quantities by drawing. define the terms speed, velocity and acceleration. plot and interpret distance-time graph and speed-time graph. determine and interpret the slope of distance- time and speed-time graph. Conceptual linkage. determine from the shape of the graph, the This unit is built on state of a body Force and Motion i. at rest - Science-IV This unit leads to: ii. moving with constant speed Motion and force - Physics-X iii. moving with variable speed. Physics IX 28 Unit 2: Kinematics calculate the area under speed-time graph to determine the distance travelled by the moving Major Concepts body. 2.1 Rest and motion derive equations of motion for a body moving 2.2 Types of motion with uniform acceleration in a straight line (Translator/, rotatory, using graph. vibratory) solve problems related to uniformly accelerated 2.3 Terms associated with motion using appropriate equations. motion; Position solve problems related to freely falling Distance and displacement bodies using 10 ms-2 as the acceleration due to Speed and velocity gravity. Acceleration INVESTIGATION SKILLS: 2.4 Scalars and vectors The students will be able to: 2.5 Graphical analysis of demonstrate various types of motion so as to motion; distinguish between translatory, rotatory and Distance-time graph vibratory motions. Speed-timegraph measure the average speed of a 100 m sprinter. 2.6 Equations of Motion; SCIENCE, TECHNOLOGY AND SOCIETY CONNECTION: The students will be able to: 2.7 Motion due to gravity list the effects of various means of transportation and their safety issues. the use of mathematical slopes (ramps) of graphs or straight lines in real life applications. interpret graph from newspaper, magazine regarding cricket and weather etc. The first thing concerning the motion of an object is its kinematics. Kinematics is the study of motion of an object without discussing the cause of motion. In this unit, we will study the types of motion, scalar and vector quantities, the relation between displacement, speed, velocity and acceleration; linear motion and equations of motion. Physics IX 29 Unit 2: Kinematics 2.1 REST AND MOTION We see various things around us. Some of them are at rest while others are in motion. A body is said to be at rest, if it does not change its position with respect to its surroundings. Surroundings are the places in its neighbourhood where various objects are present. Similarly, A body is said to be in motion, if it changes its position with Figure 2.1: The passengers in respect to its surroundings. the bus are also moving with it. The state of rest or motion of a body is relative. For example, a passenger sitting in a moving bus is at rest because he/she is not changing his/her position with respect to other passengers or objects in the bus. But to an observer outside the bus, the passengers and the objects inside the bus are in motion. 2.2 TYPES OF MOTION If we observe carefully, we will find that everything in the universe is in motion. However, different objects Figure 2.: A car and an aeroplane moving along a straight line are in move differently. Some objects move along a straight line, linear motion. some move in a curved path, and some move in some other way. There are three types of motion. (I) Translatory motion (linear, random and circular) (ii) Rotatory motion Figure 2.3: Translatory motion of (iii) Vibratory motion (to and fro motion) an object along a curved path. TRANSLATORY MOTION Watch how various objects are moving. Do they move along a straight line? Do they move along a circle? A car moving in a straight line has translational motion. Similarly, an aeroplane moving straight is in translational motion. In translational motion, a body moves along a line without any rotation. The line may be straight or curved. Figure 2.4: Translatory motion of riders in Ferris wheel. Physics IX 30 Unit 2: Kinematics The object as shown in figure 2.3 moves along a curved path without rotation. This is the translational motion of the object. Riders moving in a Ferris wheel such as shown in figure 2.4 are also in translational motion. Their motion is in a circle without rotation. Translatory motions can be divided into linear motion, circular motion and random motion. LINEAR MOTION We come across many objects which are moving in a Figure 2.5: Linear motion of the straight line. The motion of objects such as a car moving on a ball falling down. straight and level road is linear motion. Straight line motion of a body is known as its linear motion. Aeroplanes flying straight in air and objects falling vertically down are also the examples of linear motion. CIRCULAR MOTION A stone tied at the end of a string can be made to whirl. What type of path is followed by the stone? The stone as Figure 2.6: A stone tied at the shown in figure 2.6, moves in a circle and thus has circular end of a string moves in a circle. motion. The motion of an object in a circular path is known as circular motion. Figure 2.7 shows a toy train moving on a circular track. A bicycle or a car moving along a circular track possesses circular motion. Motion of the Earth around the Sun and motion of the moon around the Earth are also the Figure 2.7: A toy train moving examples of circular motions. on a circular track. Physics IX 31 Unit 2: Kinematics RANDOM MOTION Have you noticed the type of motion of insects and birds? Their movements are irregular. The disordered or irregular motion of an object is called random motion. Figure 2.8: Random motion of gas molecules is called Brownian Thus, motion of insects and birds is random motion. The motion. motion of dust or smoke particles in the air is also random motion. The Brownian motion of a gas or liquid molecules along a zig-zag path such as shown in figure 2.8 is also an example of random motion. ROTATORY MOTION Study the motion of a top. It is spinning about an axis. Particles of the spinning top move in circles and thus individual particles possess circular motion. Does the top possess circular motion? The top shown in figure 2.9 spins about its axis passing through it and thus it possesses rotatory motion. An axis is a line around which a body rotates. In circular motion, the point about which a body goes around, is outside the body. In rotatory motion, the line, around which a body moves about, is passing through the body itself. Can you spin a ball at the tip of the finger? The spinning motion of a body about its axis is called its rotatory motion. Can you point out some more differences in circular and rotatory motion? The motion of a wheel about its axis and that of a Figure 2.9: Rotatory motion steering wheel are the examples of rotatory motion. The motion of the Earth around the Sun is circular motion and not the spinning motion. However, the motion of the Earth about its geographic axis that causes day and night is rotatory motion. Think of some more examples of rotatory motion. Physics IX 32 Unit 2: Kinematics VIBRATORY MOTION Consider a baby in a swing as shown in figure 2.10. As it is pushed, the swing moves back and forth about its mean position. The motion of the baby repeats from one extreme to the other extreme with the swing. Figure2.10: Vibratory Figure2.11: Vibratory motion of a child and a motion of the pendulum To and fro motion of a body swing.. of a clock. about its mean position is known as vibratory motion. Figure 2.11 shows to and fro motion of the pendulum of a clock about its mean position, it is called vibratory motion. We can find many examples of vibratory motion around us. Look at the children in a see-saw as shown in figure 2.12. How the children Mini Exercise move as they play the see-saw game? Do they 1. When a body is said to be at possess vibratory motion as they move the see-saw? rest? 2. Give an example of a body that is at rest and is in motion at the same time. 3. Mention the type of motion in each of the following: (i) A ball moving vertically upward. (ii) A child moving down a slide. (iii) Movement of a player in a football ground. (iv) The flight of a butterfly. (v) An athlete running in a circular track. Figure 2.12: Vibratory motion of children in a see-saw. (vi) The motion of a wheel. A baby in a cradle moving to and fro, to and fro (vii) The motion of a cradle. motion of the hammer of a ringing electric bell and the motion of the string of a sitar are some of the examples of vibratory motion.  Physics IX 33 Unit 2: Kinematics 2.3 SCALARS AND VECTORS In Physics, we come across various quantities such as mass, length, volume, density, speed and force etc. We divide them into scalars and vectors. SCALARS A physical quantity which can be completely described by its magnitude is called a scalar. The magnitude of a quantity means its numerical value with an appropriate unit such as 2.5 kg, 40 s, 1.8 m, etc. Examples of scalars are mass, length, time, speed, volume, work and energy. A scalar quantity is described completely by its magnitude only. VECTORS A vector can be described completely by magnitude alongwith its direct