Chapter 3: Atoms and Molecules PDF

C hapter 3 ATOMS AND MOLECULES Ancient Indian and Greek philosophers have much experimentations by Lavoisier and always wondered about the unknown and Joseph L. Proust. unseen form of matter. The idea of divisibility...

C hapter 3 ATOMS AND MOLECULES Ancient Indian and Greek philosophers have much experimentations by Lavoisier and always wondered about the unknown and Joseph L. Proust. unseen form of matter. The idea of divisibility of matter was considered long back in India, 3.1.1 LAW OF CONSERVATION OF MASS around 500 BC. An Indian philosopher Maharishi Kanad, postulated that if we go on Is there a change in mass when a chemical dividing matter (padarth), we shall get smaller change (chemical reaction) takes place? and smaller particles. Ultimately, a stage will come when we shall come across the smallest Activity ______________ 3.1 particles beyond which further division will Take one of the following sets, X and Y not be possible. He named these particles of chemicals— Parmanu. Another Indian philosopher, X Y Pakudha Katyayama, elaborated this doctrine (i) copper sulphate sodium carbonate and said that these particles normally exist in a combined form which gives us various (ii) barium chloride sodium sulphate forms of matter. Around the same era, ancient Greek (iii) lead nitrate sodium chloride philosophers – Democritus and Leucippus Prepare separately a 5% solution of suggested that if we go on dividing matter, a any one pair of substances listed stage will come when particles obtained under X and Y each in 10 mL in water. cannot be divided further. Democritus called Take a little amount of solution of Y in these indivisible particles atoms (meaning a conical flask and some solution of indivisible). All this was based on X in an ignition tube. philosophical considerations and not much Hang the ignition tube in the flask experimental work to validate these ideas carefully; see that the solutions do not could be done till the eighteenth century. get mixed. Put a cork on the flask By the end of the eighteenth century, (see Fig. 3.1). scientists recognised the difference between elements and compounds and naturally became interested in finding out how and why elements combine and what happens when they combine. Antoine L. Lavoisier laid the foundation of chemical sciences by establishing two important laws of chemical combination. 3.1 Laws of Chemical Combination The following two laws of chemical Fig. 3.1: Ignition tube containing solution of X, dipped combination were established after in a conical flask containing solution of Y Rationalised 2023-24  Weigh the flask with its contents conservation of mass and the law of carefully. definite proportions. Now tilt and swirl the flask, so that the solutions X and Y get mixed. John Dalton was born in Weigh again. a poor weaver’s family in What happens in the reaction flask? 1766 in England. He Do you think that a chemical reaction began his career as a has taken place? teacher at the age of Why should we put a cork on the mouth twelve. Seven years later of the flask? he became a school Does the mass of the flask and its principal. In 1793, Dalton contents change? left for Manchester to teach mathematics, John Dalton Law of conservation of mass states that physics and chemistry in mass can neither be created nor destroyed in a college. He spent most of his life there a chemical reaction. teaching and researching. In 1808, he presented his atomic theory which was a 3.1.2 LAW OF CONSTANT PROPORTIONS turning point in the study of matter. Lavoisier, along with other scientists, noted that many compounds were composed of two According to Dalton’s atomic theory, all or more elements and each such compound matter, whether an element, a compound or had the same elements in the same a mixture is composed of small particles called proportions, irrespective of where the atoms. The postulates of this theory may be compound came from or who prepared it. stated as follows: In a compound such as water, the ratio of (i) All matter is made of very tiny particles the mass of hydrogen to the mass of oxygen is called atoms, which participate in always 1:8, whatever the source of water. Thus, chemical reactions. if 9 g of water is decomposed, 1 g of hydrogen (ii) Atoms are indivisible particles, which and 8 g of oxygen are always obtained. cannot be created or destroyed in a Similarly in ammonia, nitrogen and hydrogen chemical reaction. are always present in the ratio 14:3 by mass, (iii) Atoms of a given element are identical whatever the method or the source from which in mass and chemical properties. it is obtained. (iv) Atoms of different elements have This led to the law of constant proportions dif ferent masses and chemical which is also known as the law of definite properties. proportions. This law was stated by Proust as (v) Atoms combine in the ratio of small “In a chemical substance the elements are whole numbers to form compounds. always present in definite proportions by (vi) The relative number and kinds of atoms are constant in a given mass”. The next problem faced by scientists was compound. You will study in the next chapter that all to give appropriate explanations of these laws. atoms are made up of still smaller particles. British chemist John Dalton provided the basic theory about the nature of matter. uestions Q Dalton picked up the idea of divisibility of matter, which was till then just a philosophy. 1. In a reaction, 5.3 g of sodium He took the name ‘atoms’ as given by the carbonate reacted with 6 g of Greeks and said that the smallest particles of acetic acid. The products were matter are atoms. His theory was based on the 2.2 g of carbon dioxide, 0.9 g laws of chemical combination. Dalton’s atomic water and 8.2 g of sodium theory provided an explanation for the law of acetate. Show that these ATOMS AND MOLECULES 27 Rationalised 2023-24  observations are in agreement We might think that if atoms are so with the law of conservation of insignificant in size, why should we care about mass. them? This is because our entire world is made sodium carbonate + acetic acid up of atoms. We may not be able to see them, → sodium acetate + carbon but they are there, and constantly affecting dioxide + water whatever we do. Through modern techniques, 2. Hydrogen and oxygen combine in we can now produce magnified images of the ratio of 1:8 by mass to form surfaces of elements showing atoms. water. What mass of oxygen gas would be required to react completely with 3 g of hydrogen gas? 3. Which postulate of Dalton’s atomic theory is the result of the law of conservation of mass? 4. Which postulate of Dalton’s atomic theory can explain the law of definite proportions? 3.2 What is an Atom? Have you ever observed a mason building walls, from these walls a room and then a Fig. 3.2: An image of the surface of silicon collection of rooms to form a building? What is the building block of the huge building? What about the building block of an ant-hill? 3.2.1 W H A T A R E THE MODERN DAY It is a small grain of sand. Similarly, the SYMBOLS OF ATOMS OF DIFFERENT building blocks of all matter are atoms. ELEMENTS ? How big are atoms? Dalton was the first scientist to use the Atoms are very small, they are smaller than symbols for elements in a very specific sense. anything that we can imagine or compare When he used a symbol for an element he with. More than millions of atoms when also meant a definite quantity of that element, stacked would make a layer barely as thick that is, one atom of that element. Berzilius as this sheet of paper. suggested that the symbols of elements be Atomic radius is measured in nanometres. made from one or two letters of the name of 1/10 9 m = 1 nm the element. 1 m = 109 nm Relative Sizes Radii (in m) Example 10–10 Atom of hydrogen 10–9 Molecule of water 10–8 Molecule of haemoglobin –4 10 Grain of sand 10–3 Ant –1 Fig. 3.3: Symbols for some elements as proposed by 10 Apple Dalton 28 SCIENCE Rationalised 2023-24  In the beginning, the names of elements passage of time and repeated usage you will were derived from the name of the place automatically be able to reproduce where they were found for the first time. For the symbols). example, the name copper was taken from Cyprus. Some names were taken from specific colours. For example, gold was taken 3.2.2 ATOMIC MASS from the English word meaning yellow. The most remarkable concept that Dalton’s Now-a-days, IUPAC (International Union of atomic theory proposed was that of the atomic Pure and Applied Chemistry) is an international scientific organisation which mass. According to him, each element had a approves names of elements, symbols and characteristic atomic mass. The theory could units. Many of the symbols are the first one explain the law of constant proportions so well or two letters of the element’s name in that scientists were prompted to measure the English. The first letter of a symbol is always atomic mass of an atom. Since determining the written as a capital letter (uppercase) and the mass of an individual atom was a relatively second letter as a small letter (lowercase). difficult task, relative atomic masses were For example determined using the laws of chemical (i) hydrogen, H combinations and the compounds formed. (ii) aluminium, Al and not AL Let us take the example of a compound, (iii) cobalt, Co and not CO. carbon monoxide (CO) formed by carbon and Symbols of some elements are formed from oxygen. It was observed experimentally that 3 the first letter of the name and a letter, g of carbon combines with 4 g of oxygen to appearing later in the name. Examples are: (i) form CO. In other words, carbon combines chlorine, Cl, (ii) zinc, Zn etc. Other symbols have been taken from the with 4/3 times its mass of oxygen. Suppose names of elements in Latin, German or Greek. we define the atomic mass unit (earlier For example, the symbol of iron is Fe from its abbreviated as ‘amu’, but according to the Latin name ferrum, sodium is Na from natrium, latest IUPAC recommendations, it is now potassium is K from kalium. Therefore, each written as ‘u’ – unified mass) as equal to the element has a name and a unique mass of one carbon atom, then we would chemical symbol. Table 3.1: Symbols for some elements Element Symbol Element Symbol Element Symbol Aluminium Al Copper Cu Nitrogen N Argon Ar Fluorine F Oxygen O Barium Ba Gold Au Potassium K Boron B Hydrogen H Silicon Si Bromine Br Iodine I Silver Ag Calcium Ca Iron Fe Sodium Na Carbon C Lead Pb Sulphur S Chlorine Cl Magnesium Mg Uranium U Cobalt Co Neon Ne Zinc Zn (The above table is given for you to refer to assign carbon an atomic mass of 1.0 u and whenever you study about elements. Do not oxygen an atomic mass of 1.33 u. However, it bother to memorise all in one go. With the is more convenient to have these numbers as ATOMS AND MOLECULES 29 Rationalised 2023-24 whole numbers or as near to a whole numbers mass of the atom, as compared to 1/12th the as possible. While searching for various mass of one carbon-12 atom. atomic mass units, scientists initially took 1/ 16 of the mass of an atom of naturally Table 3.2: Atomic masses of occurring oxygen as the unit. This was a few elements considered relevant due to two reasons: oxygen reacted with a large number of Element Atomic Mass (u) elements and formed compounds. this atomic mass unit gave masses of Hydrogen 1 most of the elements as whole numbers. Carbon 12 However, in 1961 for a universally Nitrogen 14 accepted atomic mass unit, carbon-12 isotope Oxygen 16 was chosen as the standard reference for measuring atomic masses. One atomic mass Sodium 23 unit is a mass unit equal to exactly one-twelfth Magnesium 24 (1/12th) the mass of one atom of carbon-12. Sulphur 32 The relative atomic masses of all elements have been found with respect to an atom of Chlorine 35.5 carbon-12. Calcium 40 Imagine a fruit seller selling fruits without any standard weight with him. He takes a watermelon and says, “this has a mass equal 3.2.3 HOW DO ATOMS EXIST? to 12 units” (12 watermelon units or 12 fruit mass units). He makes twelve equal pieces of Atoms of most elements are not able to exist the watermelon and finds the mass of each fruit independently. Atoms form molecules and he is selling, relative to the mass of one piece ions. These molecules or ions aggregate in of the watermelon. Now he sells his fruits by large numbers to form the matter that we can relative fruit mass unit (fmu), as in Fig. 3.4. see, feel or touch. uestions Q 1. Define the atomic mass unit. 2. Why is it not possible to see an atom with naked eyes? 3.3 What is a Molecule? A molecule is in general a group of two or more atoms that are chemically bonded together, that is, tightly held together by attractive forces. A molecule can be defined Fig. 3.4 : (a) Watermelon, (b) 12 pieces, (c) 1/12 of as the smallest particle of an element or a watermelon, (d) how the fruit seller can compound that is capable of an independent weigh the fruits using pieces of watermelon existence and shows all the properties of that substance. Atoms of the same element or of Similarly, the relative atomic mass of the different elements can join together to form atom of an element is defined as the average molecules. 30 SCIENCE Rationalised 2023-24 3.3.1 MOLECULES OF ELEMENTS Table 3.4 : Molecules of some The molecules of an element are constituted compounds by the same type of atoms. Molecules of many Compound Combining Ratio elements, such as argon (Ar), helium (He) etc. Elements by are made up of only one atom of that element. Mass But this is not the case with most of the non- Water (H2O) Hydrogen, Oxygen 1:8 metals. For example, a molecule of oxygen Ammonia (NH3) Nitrogen, Hydrogen 14:3 consists of two atoms of oxygen and hence it Carbon is known as a diatomic molecule, O2. If 3 dioxide (CO2) Carbon, Oxygen 3:8 atoms of oxygen unite into a molecule, instead of the usual 2, we get ozone, O3. The number of atoms constituting a molecule is known as Activity ______________ 3.2 its atomicity. Refer to Table 3.4 for ratio by mass of Metals and some other elements, such as atoms present in molecules and Table carbon, do not have a simple structure but 3.2 for atomic masses of elements. Find the ratio by number of the atoms of consist of a very large and indefinite number elements in the molecules of of atoms bonded together. compounds given in Table 3.4. Let us look at the atomicity of some The ratio by number of atoms for a non-metals. water molecule can be found as follows: Element Ratio Atomic Mass Simplest Table 3.3 : Atomicity of some by mass ratio/ ratio elements mass (u) atomic mass Type of Name Atomicity Element 1 H 1 1 =1 2 1 Non-Metal Argon Monoatomic 8 1 Helium Monoatomic O 8 16 = 1 16 2 Oxygen Diatomic Thus, the ratio by number of atoms for Hydrogen Diatomic water is H:O = 2:1. Nitrogen Diatomic Chlorine Diatomic 3.3.3 WHAT IS AN ION? Phosphorus Tetra-atomic Compounds composed of metals and non- Sulphur Poly-atomic metals contain charged species. The charged species are known as ions. Ions may consist of a single charged atom or a group of atoms that have a net charge on them. An ion can be negatively or positively charged. A negatively 3.3.2 MOLECULES OF COMPOUNDS charged ion is called an ‘anion’ and the Atoms of different elements join together positively charged ion, a ‘cation’. Take, for in definite proportions to form molecules example, sodium chloride (NaCl). Its of compounds. Few examples are given in constituent particles are positively charged Table 3.4. sodium ions (Na+) and negatively charged ATOMS AND MOLECULES 31 Rationalised 2023-24 chloride ions (Cl–). A group of atoms carrying learn the symbols and combining capacity of a charge is known as a polyatomic ion (Table the elements. 3.6). We shall learn more about the formation The combining power (or capacity) of an of ions in Chapter 4. element is known as its valency. Valency can be used to find out how the atoms of an Table 3.5: Some ionic compounds element will combine with the atom(s) of Ionic Constituting Ratio another element to form a chemical compound. Compound Elements by The valency of the atom of an element can be Mass thought of as hands or arms of that atom. Calcium oxide Calcium and Human beings have two arms and an oxygen 5:2 octopus has eight. If one octopus has to catch hold of a few people in such a manner that all Magnesium Magnesium the eight arms of the octopus and both arms sulphide and sulphur 3:4 of all the humans are locked, how many Sodium Sodium humans do you think the octopus can hold? chloride and chlorine 23:35.5 Represent the octopus with O and humans with H. Can you write a formula for this combination? Do you get OH4 as the formula? 3.4 Writing Chemical Formulae The subscript 4 indicates the number of The chemical formula of a compound is a humans held by the octopus. symbolic representation of its composition. The The valencies of some common ions are chemical formulae of different compounds can given in Table 3.6. We will learn more about be written easily. For this exercise, we need to valency in the next chapter. Table 3.6: Names and symbols of some ions Vale- Name of Symbol Non- Symbol Polyatomic Symbol ncy ion metallic ions element 1. Sodium Na+ Hydrogen H+ Ammonium NH4+ Potassium K+ Hydride H- Hydroxide OH– Silver Ag+ Chloride Cl- Nitrate NO3– Copper (I)* Cu+ Bromide Br- Hydrogen Iodide I– carbonate HCO3– 2. Magnesium Mg2+ Oxide O2- Carbonate CO32– Calcium Ca2+ Sulphide S2- Sulphite SO32– Zinc Zn2+ Sulphate SO42– Iron (II)* Fe2+ Copper (II)* Cu2+ 3. Aluminium Al3+ Nitride N3- Phosphate PO43– Iron (III)* Fe3+ * Some elements show more than one valency. A Roman numeral shows their valency in a bracket. 32 SCIENCE Rationalised 2023-24 The rules that you have to follow while writing 3. Formula of carbon tetrachloride a chemical formula are as follows: the valencies or charges on the ion must balance. when a compound consists of a metal and a non-metal, the name or symbol of the metal is written first. For example: calcium oxide (CaO), sodium chloride (NaCl), iron sulphide (FeS), copper oxide (CuO), etc., where oxygen, chlorine, sulphur are non- For magnesium chloride, we write the metals and are written on the right, symbol of cation (Mg2+) first followed by the whereas calcium, sodium, iron and symbol of anion (Cl-). Then their charges are copper are metals, and are written on criss-crossed to get the formula. the left. in compounds formed with polyatomic ions, 4. Formula of magnesium chloride the number of ions present in the compound is indicated by enclosing the formula of ion in a bracket and writing the number of ions outside the bracket. For example, Mg (OH)2. In case the number of polyatomic ion is one, the bracket is not Formula : MgCl2 required. For example, NaOH. Thus, in magnesium chloride, there are 3.4.1 FORMULAE OF SIMPLE COMPOUNDS two chloride ions (Cl-) for each magnesium The simplest compounds, which are made up ion (Mg2+). The positive and negative charges of two different elements are called binary must balance each other and the overall compounds. Valencies of some ions are given structure must be neutral. Note that in the in Table 3.6. You can use these to write formulae for compounds. formula, the charges on the ions are While writing the chemical formulae for not indicated. compounds, we write the constituent elements and their valencies as shown below. Then we Some more examples must crossover the valencies of the (a) Formula for aluminium oxide: combining atoms. Examples 1. Formula of hydrogen chloride Formula : Al2O3 (b) Formula for calcium oxide: Formula of the compound would be HCl. 2. Formula of hydrogen sulphide Here, the valencies of the two elements are the same. You may arrive at the formula Ca2O2. But we simplify the formula as CaO. ATOMS AND MOLECULES 33 Rationalised 2023-24  (c) Formula of sodium nitrate: following formulae: (i) Al2(SO4)3 (ii) CaCl2 (iii) K2SO4 (iv) KNO3 Formula : NaNO3 (v) CaCO3. 3. What is meant by the term (d) Formula of calcium hydroxide: chemical formula? 4. How many atoms are present in a (i) H2S molecule and (ii) PO43– ion? Formula : Ca(OH)2 3.5 Molecular Mass Note that the for mula of calcium hydroxide is Ca(OH)2 and not CaOH2. We use 3.5.1 MOLECULAR MASS brackets when we have two or more of the In section 3.2.2 we discussed the concept of same ions in the formula. Here, the bracket atomic mass. This concept can be extended around OH with a subscript 2 indicates that to calculate molecular masses. The molecular there are two hydroxyl (OH) groups joined to mass of a substance is the sum of the atomic one calcium atom. In other words, there are masses of all the atoms in a molecule of the two atoms each of oxygen and hydrogen in substance. It is therefore the relative mass of calcium hydroxide. a molecule expressed in atomic mass units (u). (e) Formula of sodium carbonate: Example 3.1 (a) Calculate the relative molecular mass of water (H 2 O). (b) Calculate the molecular mass of HNO3. Solution: Formula : Na2CO3 (a) Atomic mass of hydrogen = 1u, In the above example, brackets are not needed oxygen = 16 u if there is only one ion present. So the molecular mass of water, which (f) Formula of ammonium sulphate: contains two atoms of hydrogen and one atom of oxygen is = 2 × 1+ 1×16 = 18 u (b) The molecular mass of HNO 3 = the atomic mass of H + the atomic mass of Formula : (NH4)2SO4 N+ 3 × the atomic mass of O = 1 + 14 + 48 = 63 u Q uestions 1. Write down the formulae of (i) sodium oxide 3.5.2 FORMULA UNIT MASS (ii) aluminium chloride The formula unit mass of a substance is a sum (iii) sodium suphide of the atomic masses of all atoms in a formula (iv) magnesium hydroxide unit of a compound. Formula unit mass is 2. Write down the names of calculated in the same manner as we calculate compounds represented by the the molecular mass. The only difference is that 34 SCIENCE Rationalised 2023-24 we use the word formula unit for those uestions Q substances whose constituent particles are ions. For example, sodium chloride as 1. Calculate the molecular masses discussed above, has a formula unit NaCl. Its of H2, O2, Cl2, CO2, CH4, C2H6, formula unit mass can be calculated as– C2H4, NH3, CH3OH. 1 × 23 + 1 × 35.5 = 58.5 u 2. Calculate the for mula unit masses of ZnO, Na2O, K2CO3, Example 3.2 Calculate the formula unit given atomic masses of Zn = 65 u, mass of CaCl2. Na = 23 u, K = 39 u, C = 12 u, Solution: and O = 16 u. Atomic mass of Ca + (2 × atomic mass of Cl) = 40 + 2 × 35.5 = 40 + 71 = 111 u What you have learnt During a chemical reaction, the sum of the masses of the reactants and products remains unchanged. This is known as the Law of Conservation of Mass. In a pure chemical compound, elements are always present in a definite proportion by mass. This is known as the Law of Definite Proportions. An atom is the smallest particle of the element that cannot usually exist independently and retain all its chemical properties. A molecule is the smallest particle of an element or a compound capable of independent existence under ordinary conditions. It shows all the properties of the substance. A chemical formula of a compound shows its constituent elements and the number of atoms of each combining element. Clusters of atoms that act as an ion are called polyatomic ions. They carry a fixed charge on them. The chemical formula of a molecular compound is determined by the valency of each element. In ionic compounds, the charge on each ion is used to determine the chemical formula of the compound. ATOMS AND MOLECULES 35 Rationalised 2023-24  Exercises 1. A 0.24 g sample of compound of oxygen and boron was found by analysis to contain 0.096 g of boron and 0.144 g of oxygen. Calculate the percentage composition of the compound by weight. 2. When 3.0 g of carbon is burnt in 8.00 g oxygen, 11.00 g of carbon dioxide is produced. What mass of carbon dioxide will be formed when 3.00 g of carbon is burnt in 50.00 g of oxygen? Which law of chemical combination will govern your answer? 3. What are polyatomic ions? Give examples. 4. Write the chemical formulae of the following. (a) Magnesium chloride (b) Calcium oxide (c) Copper nitrate (d) Aluminium chloride (e) Calcium carbonate. 5. Give the names of the elements present in the following compounds. (a) Quick lime (b) Hydrogen bromide (c) Baking powder (d) Potassium sulphate. 6. Calculate the molar mass of the following substances. (a) Ethyne, C2H2 (b) Sulphur molecule, S8 (c) Phosphorus molecule, P4 (Atomic mass of phosphorus = 31) (d) Hydrochloric acid, HCl (e) Nitric acid, HNO3 Group Activity Play a game for writing formulae. Example1 : Make placards with symbols and valencies of the elements separately. Each student should hold two placards, one with the symbol in the right hand and the other with the valency in the left hand. Keeping the symbols in place, students should criss-cross their valencies to form the formula of a compound. 36 SCIENCE Rationalised 2023-24  Example 2 : A low cost model for writing formulae: Take empty blister packs of medicines. Cut them in groups, according to the valency of the element, as shown in the figure. Now, you can make formulae by fixing one type of ion into other. For example: Na+ SO 4 2- P0 43- Formula for sodium sulphate: 2 sodium ions can be fixed on one sulphate ion. Hence, the formula will be: Na2SO4 Do it yourself : Now, write the formula of sodium phosphate. ATOMS AND MOLECULES 37 Rationalised 2023-24 C hapter 9 GRAVITATION Let us try to understand the motion of the We have learnt about the motion of objects and moon by recalling activity 7.11. force as the cause of motion. We have learnt that a force is needed to change the speed or Activity ______________ 9.1 the direction of motion of an object. We always observe that an object dropped from a height Take a piece of thread. Tie a small stone at one end. Hold the falls towards the earth. We know that all the other end of the thread and whirl it planets go around the Sun. The moon goes round, as shown in Fig. 9.1. around the earth. In all these cases, there must Note the motion of the stone. be some force acting on the objects, the planets Release the thread. and on the moon. Isaac Newton could grasp Again, note the direction of motion of that the same force is responsible for all these. the stone. This force is called the gravitational force. In this chapter we shall learn about gravitation and the universal law of gravitation. We shall discuss the motion of objects under the influence of gravitational force on the earth. We shall study how the weight of a body varies from place to place. We shall also discuss the conditions for objects to float in liquids. 9.1 Gravitation We know that the moon goes around the earth. An object when thrown upwards, reaches a certain height and then falls downwards. It is said that when Newton was sitting under a tree, Fig. 9.1: A stone describing a circular path with a an apple fell on him. The fall of the apple made velocity of constant magnitude. Newton start thinking. He thought that: if the earth can attract an apple, can it not attract Before the thread is released, the stone the moon? Is the force the same in both cases? moves in a circular path with a certain speed He conjectured that the same type of force is and changes direction at every point. responsible in both the cases. He argued that The change in direction involves change in at each point of its orbit, the moon falls velocity or acceleration. The force that causes towards the earth, instead of going off in a this acceleration and keeps the body moving straight line. So, it must be attracted by the along the circular path is acting towards earth. But we do not really see the moon falling the centre. This force is called the towards the earth. centripetal (meaning ‘centre-seeking’) force. 100 SCIENCE Rationalised 2023-24 In the absence of this force, the stone flies off 9.1.1 UNIVERSAL LAW OF GRAVITATION along a straight line. This straight line will be a tangent to the circular path. Every object in the universe attracts every other object with a force which is proportional to the product of their masses and inversely Tangent to a circle proportional to the square of the distance between them. The force is along the line joining the centres of two objects. More to know A straight line that meets the circle at one and only one point is called a Mm F =G 2 tangent to the circle. Straight line d ABC is a tangent to the circle at point B. Fig. 9.2: The gravitational force between two uniform objects is directed along the line The motion of the moon around the earth joining their centres. is due to the centripetal force. The centripetal force is provided by the force of attraction of Let two objects A and B of masses M and the earth. If there were no such force, the m lie at a distance d from each other as shown moon would pursue a uniform straight line in Fig. 9.2. Let the force of attraction between motion. two objects be F. According to the universal It is seen that a falling apple is attracted law of gravitation, the force between two towards the earth. Does the apple attract the objects is directly proportional to the product earth? If so, we do not see the earth moving of their masses. That is, towards an apple. Why? F∝M × m (9.1) According to the third law of motion, the And the force between two objects is inversely apple does attract the earth. But according proportional to the square of the distance to the second law of motion, for a given force, between them, that is, acceleration is inversely proportional to the mass of an object [Eq. (8.4)]. The mass of an 1 apple is negligibly small compared to that of F∝ (9.2) d2 the earth. So, we do not see the earth moving towards the apple. Extend the same argument Combining Eqs. (10.1) and (10.2), we get for why the earth does not move towards the moon. M ×m In our solar system, all the planets go F ∝ d2 (9.3) around the Sun. By arguing the same way, we can say that there exists a force between M×m the Sun and the planets. From the above facts or, F = G 2 (9.4) d Newton concluded that not only does the earth attract an apple and the moon, but all where G is the constant of proportionality and objects in the universe attract each other. This is called the universal gravitation constant. force of attraction between objects is called By multiplying crosswise, Eq. (9.4) gives the gravitational force. F×d2=GM×m GRAVITATION 101 Rationalised 2023-24  2 From Eq. (9.4), the force exerted by the Fd or G= (9.5) earth on the moon is M×m M ×m The SI unit of G can be obtained by F =G d2 substituting the units of force, distance and mass in Eq. (9.5) as N m2 kg–2. 6.7 × 10 −11 N m 2 kg -2 × 6 × 1024 kg × 7.4 × 1022 kg = The value of G was found out by (3.84 × 108 m)2 Henry Cavendish (1731 – 1810) by using a = 2.02 × 1020 N. sensitive balance. The accepted value of G is 6.673 × 10–11 N m2 kg–2. Thus, the force exerted by the earth on We know that there exists a force of the moon is 2.02 × 1020 N. attraction between any two objects. Compute the value of this force between you and your Q friend sitting closeby. Conclude how you do uestions not experience this force! 1. State the universal law of gravitation. 2. Write the formula to find the The law is universal in the sense that magnitude of the gravitational it is applicable to all bodies, whether force between the earth and an the bodies are big or small, whether object on the surface of the earth. More to know they are celestial or terrestrial. Inverse-square 9.1.2 IMPORTANCE OF THE UNIVERSAL LAW OF GRAVITATION Saying that F is inversely proportional to the square of d The universal law of gravitation successfully means, for example, that if d gets explained several phenomena which were bigger by a factor of 6, F becomes believed to be unconnected: 1 (i) the force that binds us to the earth; times smaller. (ii) the motion of the moon around the 36 earth; (iii) the motion of planets around the Sun; and Example 9.1 The mass of the earth is (iv) the tides due to the moon and the Sun. 6 × 1024 kg and that of the moon is 7.4 × 1022 kg. If the distance between the 9.2 Free Fall earth and the moon is 3.84×105 km, calculate the force exerted by the earth on Let us try to understand the meaning of free the moon. (Take G = 6.7 × 10–11 N m2 kg-2) fall by performing this activity. Solution: Activity ______________ 9.2 The mass of the earth, M = 6 × 1024 kg Take a stone. The mass of the moon, Throw it upwards. m = 7.4 × 1022 kg It reaches a certain height and then it starts falling down. The distance between the earth and the moon, We have learnt that the earth attracts d = 3.84 × 105 km objects towards it. This is due to the = 3.84 × 105 × 1000 m gravitational force. Whenever objects fall = 3.84 × 108 m towards the earth under this force alone, we G = 6.7 × 10–11 N m2 kg–2 say that the objects are in free fall. Is there any 102 SCIENCE Rationalised 2023-24 change in the velocity of falling objects? While calculations, we can take g to be more or less falling, there is no change in the direction of constant on or near the earth. But for objects motion of the objects. But due to the earth’s far from the earth, the acceleration due to attraction, there will be a change in the gravitational force of earth is given by magnitude of the velocity. Any change in Eq. (9.7). velocity involves acceleration. Whenever an object falls towards the earth, an acceleration 9.2.1 TO CALCULATE THE VALUE OF g is involved. This acceleration is due to the earth’s gravitational force. Therefore, this To calculate the value of g, we should put the acceleration is called the acceleration due to values of G, M and R in Eq. (9.9), namely, the gravitational force of the earth (or universal gravitational constant, G = 6.7 × 10– acceleration due to gravity). It is denoted by 11 N m2 kg-2, mass of the earth, M = 6 × 1024 kg, g. The unit of g is the same as that of and radius of the earth, R = 6.4 × 106 m. acceleration, that is, m s–2. M We know from the second law of motion g=G 2 that force is the product of mass and R acceleration. Let the mass of the stone in 6.7 × 10-11 N m 2 kg -2 × 6 × 1024 kg activity 9.2 be m. We already know that there = is acceleration involved in falling objects due (6.4 × 106 m)2 to the gravitational force and is denoted by g. = 9.8 m s–2. Therefore the magnitude of the gravitational force F will be equal to the product of mass Thus, the value of acceleration due to gravity and acceleration due to the gravitational of the earth, g = 9.8 m s–2. force, that is, F=mg (9.6) 9.2.2 MOTION OF OBJECTS UNDER THE From Eqs. (9.4) and (9.6) we have INFLUENCE OF GRAVITATIONAL M ×m FORCE OF THE EARTH mg =G 2 d Let us do an activity to understand whether all objects hollow or solid, big or small, will M fall from a height at the same rate. or g = G 2 (9.7) d where M is the mass of the earth, and d is the Activity ______________ 9.3 distance between the object and the earth. Take a sheet of paper and a stone. Let an object be on or near the surface of Drop them simultaneously from the the earth. The distance d in Eq. (9.7) will be first floor of a building. Observe equal to R, the radius of the earth. Thus, for whether both of them reach the objects on or near the surface of the earth, ground simultaneously. We see that paper reaches the ground M ×m mg = G (9.8) little later than the stone. This happens 2 R because of air resistance. The air offers resistance due to friction to the motion M of the falling objects. The resistance g=G (9.9) R 2 offered by air to the paper is more than the resistance offered to the stone. If The earth is not a perfect sphere. As the we do the experiment in a glass jar radius of the earth increases from the poles to from which air has been sucked out, the equator, the value of g becomes greater at the paper and the stone would fall at the poles than at the equator. For most the same rate. GRAVITATION 103 Rationalised 2023-24  We know that an object experiences u +v acceleration during free fall. From Eq. (9.9), (ii) average speed = 2 this acceleration experienced by an object is = (0 m s–1+ 5 m s–1)/2 independent of its mass. This means that all = 2.5 m s–1 objects hollow or solid, big or small, should (iii) distance travelled, s = ½ a t2 fall at the same rate. According to a story, = ½ × 10 m s–2 × (0.5 s)2 Galileo dropped different objects from the top = ½ × 10 m s–2 × 0.25 s2 of the Leaning Tower of Pisa in Italy to prove = 1.25 m the same. Thus, As g is constant near the earth, all the (i) its speed on striking the ground equations for the uniformly accelerated = 5 m s–1 motion of objects become valid with (ii) its average speed during the 0.5 s acceleration a replaced by g. = 2.5 m s–1 The equations are: (iii) height of the ledge from the ground v = u + at (9.10) = 1.25 m. 1 s = ut + at2 (9.11) 2 v2 = u2 + 2as (9.12) Example 9.3 An object is thrown vertically upwards and rises to a height of 10 m. where u and v are the initial and final velocities Calculate (i) the velocity with which the and s is the distance covered in time, t. object was thrown upwards and (ii) the In applying these equations, we will take time taken by the object to reach the acceleration, a to be positive when it is in the highest point. direction of the velocity, that is, in the direction of motion. The acceleration, a will Solution: be taken as negative when it opposes the motion. Distance travelled, s = 10 m Final velocity, v = 0 m s–1 Acceleration due to gravity, g = 9.8 m s–2 Example 9.2 A car falls off a ledge and Acceleration of the object, a = –9.8 m s–2 drops to the ground in 0.5 s. Let (upward motion) g = 10 m s –2 (for simplifying the (i) v 2 = u2 + 2a s calculations). 0 = u 2 + 2 × (–9.8 m s–2) × 10 m (i) What is its speed on striking the –u 2 = –2 × 9.8 × 10 m2 s–2 ground? u = 196 m s-1 (ii) What is its average speed during the 0.5 s? u = 14 m s-1 (iii) How high is the ledge from the (ii) v=u+at ground? 0 = 14 m s–1 – 9.8 m s–2 × t t = 1.43 s. Solution: Thus, (i) Initial velocity, u = 14 m s–1, and Time, t = ½ second (ii) Time taken, t = 1.43 s. Initial velocity, u = 0 m s–1 Acceleration due to gravity, g = 10 m s–2 Q Acceleration of the car, a = + 10 m s–2 uestions (downward) 1. What do you mean by free fall? (i) speed v = at 2. What do you mean by acceleration v = 10 m s–2 × 0.5 s due to gravity? = 5 m s–1 104 SCIENCE Rationalised 2023-24 9.3 Mass attracts the object. In the same way, the weight of an object on the moon is the force with We have learnt in the previous chapter that the which the moon attracts that object. The mass mass of an object is the measure of its inertia. of the moon is less than that of the earth. Due We have also learnt that greater the mass, the to this the moon exerts lesser force of attraction greater is the inertia. It remains the same on objects. whether the object is on the earth, the moon Let the mass of an object be m. Let its or even in outer space. Thus, the mass of an weight on the moon be Wm. Let the mass of object is constant and does not change from the moon be Mm and its radius be Rm. place to place. By applying the universal law of gravitation, the weight of the object on the moon will be 9.4 Weight Mm × m Wm = G (9.16) We know that the earth attracts every object Rm2 with a certain force and this force depends on Let the weight of the same object on the the mass (m) of the object and the acceleration earth be We. The mass of the earth is M and its due to the gravity (g). The weight of an object radius is R. is the force with which it is attracted towards the earth. Table 9.1 We know that F = m × a, (9.13) Celestial Mass (kg) Radius (m) that is, body F = m × g. (9.14) The force of attraction of the earth on an Earth 5.98 × 1024 6.37 ××106 object is known as the weight of the object. It Moon 7.36 ××1022 1.74 ××106 is denoted by W. Substituting the same in Eq. (9.14), we have W=m×g (9.15) From Eqs. (9.9) and (9.15) we have, As the weight of an object is the force with M ×m We = G (9.17) which it is attracted towards the earth, the SI R2 unit of weight is the same as that of force, that Substituting the values from Table 10.1 in is, newton (N). The weight is a force acting Eqs. (9.16) and (9.17), we get vertically downwards; it has both magnitude and direction. 7.36 × 1022 kg × m Wm = G We have learnt that the value of g is (1.74 × 10 m ) 6 2 constant at a given place. Therefore at a given place, the weight of an object is directly Wm = 2.431 × 1010 G × m (9.18a) proportional to the mass, say m, of the object, and We = 1.474 × 10 G × m 11 (9.18b) that is, W ∝ m. It is due to this reason that at a given place, we can use the weight of an Dividing Eq. (9.18a) by Eq. (9.18b), we get object as a measure of its mass. The mass of Wm 2.431 × 1010 an object remains the same everywhere, that = is, on the earth and on any planet whereas its We 1.474 × 1011 weight depends on its location because g Wm 1 depends on location. or W = 0.165 ≈ 6 (9.19) e 9.4.1 W EIGHT OF AN OBJECT ON Weight of the object on the moon = 1 THE MOON Weight of the object on the earth 6 We have learnt that the weight of an object on Weight of the object on the moon the earth is the force with which the earth = (1/6) × its weight on the earth. GRAVITATION 105 Rationalised 2023-24  of the net force in a particular direction (thrust) Example 9.4 Mass of an object is 10 kg. and the force per unit area (pressure) acting What is its weight on the earth? on the object concerned. Solution: Let us try to understand the meanings of Mass, m = 10 kg thrust and pressure by considering the Acceleration due to gravity, g = 9.8 m s–2 following situations: W=m×g Situation 1: You wish to fix a poster on a W = 10 kg × 9.8 m s-2 = 98 N bulletin board, as shown in Fig 9.3. To do this Thus, the weight of the object is 98 N. task you will have to press drawing pins with your thumb. You apply a force on the surface area of the head of the pin. This force is directed Example 9.5 An object weighs 10 N when perpendicular to the surface area of the board. measured on the surface of the earth. This force acts on a smaller area at the tip of What would be its weight when the pin. measured on the surface of the moon? Solution: We know, Weight of object on the moon = (1/6) × its weight on the earth. That is, W 10 Wm = e = N. 6 6 = 1.67 N. Thus, the weight of object on the surface of the moon would be 1.67 N. Q uestions 1. What are the differences between the mass of an object and its weight? 2. Why is the weight of an object on 1 th the moon its weight on the 6 earth? 9.5 Thrust and Pressure Fig. 9.3: To fix a poster, drawing pins are pressed with the thumb perpendicular to the board. Have you ever wondered why a camel can run in a desert easily? Why an army tank weighing more than a thousand tonne rests upon a Situation 2: You stand on loose sand. Your continuous chain? Why a truck or a motorbus feet go deep into the sand. Now, lie down on has much wider tyres? Why cutting tools have the sand. You will find that your body will not sharp edges? In order to address these go that deep in the sand. In both cases the questions and understand the phenomena force exerted on the sand is the weight of your involved, it helps to introduce the concepts body. 106 SCIENCE Rationalised 2023-24  You have learnt that weight is the force by the wooden block on the table top if acting vertically downwards. Here the force is it is made to lie on the table top with its acting perpendicular to the surface of the sand. sides of dimensions (a) 20 cm × 10 cm The force acting on an object perpendicular to and (b) 40 cm × 20 cm. the surface is called thrust. When you stand on loose sand, the force, Solution: that is, the weight of your body is acting on The mass of the wooden block = 5 kg an area equal to area of your feet. When you The dimensions lie down, the same force acts on an area equal = 40 cm × 20 cm × 10 cm to the contact area of your whole body, which Here, the weight of the wooden block is larger than the area of your feet. Thus, the effects of forces of the same magnitude on applies a thrust on the table top. different areas are different. In the above That is, cases, thrust is the same. But effects are Thrust = F = m × g different. Therefore the effect of thrust = 5 kg × 9.8 m s–2 depends on the area on which it acts. = 49 N The effect of thrust on sand is larger while Area of a side = length × breadth standing than while lying. The thrust on unit = 20 cm × 10 cm = 200 cm2 = 0.02 m2 area is called pressure. Thus, From Eq. (9.20), thrust Pressure = (9.20) 49 N area Pressure = 0.02 m 2 Substituting the SI unit of thrust and area in Eq. (9.20), we get the SI unit of pressure as N/ = 2450 N m-2. m2 or N m–2. When the block lies on its side of In honour of scientist Blaise Pascal, the dimensions 40 cm × 20 cm, it exerts SI unit of pressure is called pascal, denoted the same thrust. as Pa. Area= length × breadth Let us consider a numerical example to = 40 cm × 20 cm understand the effects of thrust acting on = 800 cm2 = 0.08 m2 different areas. From Eq. (9.20), 49 N Example 9.6 A block of wood is kept on a Pressure = 0.08 m 2 tabletop. The mass of wooden block is 5 kg and its dimensions are 40 cm × 20 = 612.5 N m–2 cm × 10 cm. Find the pressure exerted The pressure exerted by the side 20 cm × 10 cm is 2450 N m–2 and by the side 40 cm × 20 cm is 612.5 N m–2. Thus, the same force acting on a smaller area exerts a larger pressure, and a smaller pressure on a larger area. This is the reason why a nail has a pointed tip, knives have sharp edges and buildings have wide foundations. 9.5.1 PRESSURE IN FLUIDS All liquids and gases are fluids. A solid exerts pressure on a surface due to its weight. Fig. 9.4 Similarly, fluids have weight, and they also GRAVITATION 107 Rationalised 2023-24 exert pressure on the base and walls of the water on the bottle is greater than its weight. container in which they are enclosed. Pressure Therefore it rises up when released. exerted in any confined mass of fluid is To keep the bottle completely immersed, transmitted undiminished in all directions. the upward force on the bottle due to water must be balanced. This can be achieved by 9.5.2 BUOYANCY an externally applied force acting downwards. This force must at least be equal to the Have you ever had a swim in a pool and felt difference between the upward force and the lighter? Have you ever drawn water from a weight of the bottle. well and felt that the bucket of water is heavier The upward force exerted by the water on when it is out of the water? Have you ever the bottle is known as upthrust or buoyant wondered why a ship made of iron and steel force. In fact, all objects experience a force of does not sink in sea water, but while the same buoyancy when they are immersed in a fluid. amount of iron and steel in the form of a sheet The magnitude of this buoyant force depends would sink? These questions can be answered on the density of the fluid. by taking buoyancy in consideration. Let us understand the meaning of buoyancy by 9.5.3 W HY OBJECTS FLOAT OR SINK doing an activity. WHEN PLACED ON THE SURFACE OF Activity ______________ 9.4 WATER? Take an empty plastic bottle. Close Let us do the following activities to arrive at the mouth of the bottle with an an answer for the above question. airtight stopper. Put it in a bucket filled with water. You see that the Activity ______________ 9.5 bottle floats. Push the bottle into the water. You feel Take a beaker filled with water. an upward push. Try to push it further Take an iron nail and place it on the down. You will find it difficult to push surface of the water. deeper and deeper. This indicates that Observe what happens. water exerts a force on the bottle in the upward direction. The upward force The nail sinks. The force due to the exerted by the water goes on increasing gravitational attraction of the earth on the as the bottle is pushed deeper till it is iron nail pulls it downwards. There is an completely immersed. upthrust of water on the nail, which pushes Now, release the bottle. It bounces it upwards. But the downward force acting back to the surface. on the nail is greater than the upthrust of Does the force due to the gravitational water on the nail. So it sinks (Fig. 9.5). attraction of the earth act on this bottle? If so, why doesn’t the bottle stay immersed in water after it is released? How can you immerse the bottle in water? The force due to the gravitational attraction of the earth acts on the bottle in the downward direction. So the bottle is pulled downwards. But the water exerts an upward force on the bottle. Thus, the bottle is pushed upwards. We have learnt that weight of an object is the force due to gravitational attraction of the earth. When the bottle is Fig. 9.5: An iron nail sinks and a cork floats when immersed, the upward force exerted by the placed on the surface of water. 108 SCIENCE Rationalised 2023-24  Activity ______________ 9.6 Take a beaker filled with water. Take a piece of cork and an iron nail of equal mass. Place them on the surface of water. Observe what happens. The cork floats while the nail sinks. This happens because of the difference in their densities. The density of a substance is defined as the mass per unit volume. The (a) density of cork is less than the density of water. This means that the upthrust of water on the cork is greater than the weight of the cork. So it floats (Fig. 9.5). (b) The density of an iron nail is more than the density of water. This means that the Fig. 9.6: (a) Observe the elongation of the rubber string due to the weight of a piece of stone upthrust of water on the iron nail is less than suspended from it in air. (b) The elongation the weight of the nail. So it sinks. decreases as the stone is immersed Therefore objects of density less than that in water. of a liquid float on the liquid. The objects of density greater than that of a liquid sink in Observe what happens to elongation the liquid. of the string or the reading on the balance. Q uestions You will find that the elongation of the string 1. Why is it difficult to hold a school or the reading of the balance decreases as the bag having a strap made of a thin stone is gradually lowered in the water. However, and strong string? no further change is observed once the stone 2. What do you mean by buoyancy? gets fully immersed in the water. What do you 3. Why does an object float or sink infer from the decrease in the extension of the when placed on the surface of string or the reading of the spring balance? water? We know that the elongation produced in the string or the spring balance is due to the 9.6 Archimedes’ Principle weight of the stone. Since the extension decreases once the stone is lowered in water, it means that some force acts on the stone in Activity ______________ 9.7 upward direction. As a result, the net force on Take a piece of stone and tie it to one the string decreases and hence the elongation end of a rubber string or a spring also decreases. As discussed earlier, this balance. upward force exerted by water is known as Suspend the stone by holding the the force of buoyancy. balance or the string as shown in What is the magnitude of the buoyant Fig. 9.6 (a). Note the elongation of the string or force experienced by a body? Is it the same the reading on the spring balance due in all fluids for a given body? Do all bodies to the weight of the stone. in a given fluid experience the same buoyant Now, slowly dip the stone in the water force? The answer to these questions is in a container as shown in contained in Archimedes’ principle, stated as Fig. 9.6 (b). follows: GRAVITATION 109 Rationalised 2023-24  When a body is immersed fully or partially Archimedes’ principle has many in a fluid, it experiences an upward force that applications. It is used in designing ships and is equal to the weight of the fluid displaced submarines. Lactometers, which are used to by it. determine the purity of a sample of milk and Now, can you explain why a further hydrometers used for determining density of decrease in the elongation of the string was liquids, are based on this principle. not observed in activity 9.7, as the stone was Q fully immersed in water? uestions Archimedes was a Greek scientist. He 1. You find your mass to be 42 kg discovered the principle, subsequently named on a weighing machine. Is your after him, after noticing that mass more or less than 42 kg? the water in a bathtub 2. You have a bag of cotton and an overflowed when he stepped iron bar, each indicating a mass into it. He ran through the of 100 kg when measured on a streets shouting “Eureka!”, weighing machine. In reality, which means “I have got it”. one is heavier than other. Can This knowledge helped him to you say which one is heavier determine the purity of the and why? Archimedes gold in the crown made for the king. His work in the field of Geometry and Mechanics made him famous. His understanding of levers, pulleys, wheels- and-axle helped the Greek army in its war with Roman army. What you have learnt The law of gravitation states that the force of attraction between any two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them. The law applies to objects anywhere in the universe. Such a law is said to be universal. Gravitation is a weak force unless large masses are involved. The force of gravity decreases with altitude. It also varies on the surface of the earth, decreasing from poles to the equator. The weight of a body is the force with which the earth attracts it. The weight is equal to the product of mass and acceleration due to gravity. The weight may vary from place to place but the mass stays constant. 110 SCIENCE Rationalised 2023-24  All objects experience a force of buoyancy when they are immersed in a fluid. Objects having density less than that of the liquid in which they are immersed, float on the surface of the liquid. If the density of the object is more than the density of the liquid in which it is immersed then it sinks in the liquid. Exercises 1. How does the force of gravitation between two objects change when the distance between them is reduced to half ? 2. Gravitational force acts on all objects in proportion to their masses. Why then, a heavy object does not fall faster than a light object? 3. What is the magnitude of the gravitational force between the earth and a 1 kg object on its surface? (Mass of the earth is 6 × 1024 kg and radius of the earth is 6.4 × 106 m.) 4. The earth and the moon are attracted to each other by gravitational force. Does the earth attract the moon with a force that is greater or smaller or the same as the force with which the moon attracts the earth? Why? 5. If the moon attracts the earth, why does the earth not move towards the moon? 6. What happens to the force between two objects, if (i) the mass of one object is doubled? (ii) the distance between the objects is doubled and tripled? (iii) the masses of both objects are doubled? 7. What is the importance of universal law of gravitation? 8. What is the acceleration of free fall? 9. What do we call the gravitational force between the earth and an object? 10. Amit buys few grams of gold at the poles as per the instruction of one of his friends. He hands over the same when he meets him at the equator. Will the friend agree with the weight of gold bought? If not, why? [Hint: The value of g is greater at the poles than at the equator.] 11. Why will a sheet of paper fall slower than one that is crumpled into a ball? 1 12. Gravitational force on the surface of the moon is only as 6 strong as gravitational force on the earth. What is the weight in newtons of a 10 kg object on the moon and on the earth? GRAVITATION 111 Rationalised 2023-24  13. A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate (i) the maximum height to which it rises, (ii) the total time it takes to return to the surface of the earth. 14. A stone is released from the top of a tower of height 19.6 m. Calculate its final velocity just before touching the ground. 15. A stone is thrown vertically upward with an initial velocity of 40 m/s. Taking g = 10 m/s2, find the maximum height reached by the stone. What is the net displacement and the total distance covered by the stone? 16. Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth = 6 × 1024 kg and of the Sun = 2 × 1030 kg. The average distance between the two is 1.5 × 1011 m. 17. A stone is allowed to fall from the top of a tower 100 m high and at the same time another stone is projected vertically upwards from the ground with a velocity of 25 m/s. Calculate when and where the two stones will meet. 18. A ball thrown up vertically returns to the thrower after 6 s. Find (a) the velocity with which it was thrown up, (b) the maximum height it reaches, and (c) its position after 4 s. 19. In what direction does the buoyant force on an object immersed in a liquid act? 20. Why does a block of plastic released under water come up to the surface of water? 21. The volume of 50 g of a substance is 20 cm3. If the density of water is 1 g cm–3, will the substance float or sink? 22. The volume of a 500 g sealed packet is 350 cm3. Will the packet float or sink in water if the density of water is 1 g cm–3? What will be the mass of the water displaced by this packet? 112 SCIENCE Rationalised 2023-24 C hapter 12 IMPROVEMENT IN FOOD RESOURCES We know that all living organisms need food. disturbing the balances maintaining it. Hence, Food supplies proteins, carbohydrates, fats, there is a need for sustainable practices in vitamins and minerals, all of which we require agriculture and animal husbandry. for body development, growth and health. Also, simply increasing grain production Both plants and animals are major sources for storage in warehouses cannot solve the of food for us. We obtain most of this food problem of malnutrition and hunger. People from agriculture and animal husbandry. should have money to purchase food. Food We read in newspapers that efforts are security depends on both availability of food always being made to improve production and access to it. The majority of our from agriculture and animal husbandry. Why population depends on agriculture for their is this necessary? Why we cannot make do livelihood. Increasing the incomes of people with the current levels of production? working in agriculture is therefore necessary India is a very populous country. Our to combat the problem of hunger. Scientific population is more than one billion people, management practices should be undertaken and it is still growing. As food for this growing to obtain high yields from farms. For population, we will soon need more than a sustained livelihood, one should undertake quarter of a billion tonnes of grain every year. mixed farming, intercropping, and integrated This can be done by farming on more land. farming practices, for example, combine But India is already intensively cultivated. As agriculture with livestock/poultry/fisheries/ a result, we do not have any major scope for bee-keeping. increasing the area of land under cultivation. The question thus becomes – how do we Therefore, it is necessary to increase our increase the yields of crops and livestock? production efficiency for both crops and livestock. 12.1 Improvement in Crop Yields Efforts to meet the food demand by increasing food production have led to some Cereals such as wheat, rice, maize, millets and successes so far. We have had the green sorghum provide us carbohydrate for energy revolution, which contributed to increased requirement. Pulses like gram (chana), pea food-grain production. We have also had the (matar), black gram (urad), green gram (moong), white revolution, which has led to better and pigeon pea (arhar), lentil (masoor), provide us with more efficient use as well as availability of milk. protein. And oil seeds including soyabean, However, these revolutions mean that our ground nut, sesame, castor, mustard, linseed and natural resources are getting used more sunflower provide us with necessary fats (Fig. intensively. As a result, there are more 12.1). Vegetables, spices and fruits provide a chances of causing damage to our natural range of vitamins and minerals in addition to resources to the point of destroying their small amounts of proteins, carbohydrates and balance completely. Therefore, it is important fats. In addition to these food crops, fodder crops that we should increase food production like berseem, oats or sudan grass are raised as without degrading our environment and food for the livestock. 140 SCIENCE Rationalised 2023-24  the kharif season from the month of June to October, and some of the crops are grown in the winter season, called the rabi season from November to April. Paddy, soyabean, pigeon pea, maize, cotton, green gram and black gram are kharif crops, whereas wheat, gram, peas, mustard, linseed are rabi crops. In India there has been a four times increase in the production of food grains from 1952 to 2010 with only 25% increase in the cultivable land area. How has this increase in production been achieved? If we think of the practices involved in farming, we can see that we can divide it into three stages. The first is the choice of seeds for planting. The second is the nurturing of the crop plants. The third is the protection of the growing and harvested crops from loss. Thus, the major groups of activities for improving crop yields can be classified as: Crop variety improvement Crop production improvement Crop protection management. 12.1.1 CROP VARIETY IMPROVEMENT This approach depends