202110208-APEX-STUDENT-WORKBOOK-PHYSICAL_SCIENCE-G09-PART2

3.2 Terminology i. Centre of gravity – The center of gravity is the point where total weight of the body acts. ii. Stability – The state of the body when both center of mass and center of gravity coincide. 3.3 Key Concepts i. The point through which the total weight of the body acts is called the centre of gravity. ii. If the weight vector passes through the base of the body then the body will be in equilibrium. 3.4 Conceptual Understanding Q1. Explain some situations where center of gravity of man lies outside the body. [Refer to TB page 139 Q6] A. Centre of gravity of a human being is located interior to the second sacral vertebra. Centre of gravity of man lies outside the body in the following situations: 1. While walking with one leg. 2. While carrying a load like bucket full of water with one hand. 3˙ While doing sit - ups. 3.5 Asking Questions and Making Hypothesis Q1. Where does the center of gravity of the atmosphere of the earth lie? [Refer to TB page 139 Q9] A. The earth’s atmosphere is about 11,000 km thick, but most of its bulk is contained in the first 11 km above the earth’s surface. Since the earth and its atmosphere are roughly spherical, the centre of the earth is also the centre of gravtity of the earth’s atmosphere. 3.6 Experimentation and Field Investigation Q1. How can you find out the centre of gravity of India map made with steel? Explain. [Refer to TB page 139 Q10] A. We can find the centre of gravity of our India map by trying to balance the map on our finger. The point where the map balances will be its centre of gravity. SESSION 3. CENTRE OF GRAVITY 49

3.7 Application to Daily Life, Concern to Bio Diversity Q1. A man is standing against a wall such that his right shoulder and right leg are in contact with the surface of the wall along his height. Can he raise his left leg at this position without moving his body away from the wall? Why? Explain. [Refer to TB page 139 Q13] A. i. He can’t raise his left leg in this position without moving his body away from the wall. ii. As we try to raise the left leg the centre of gravity doesn’t fall inside the base. So we have to move our body away from the wall to make the weight vector of the body to fall within base. Q2. Where does the center of gravity lie when a boy is doing sit–ups? Does weight vector pass through the base or move away from the base? [Refer to TB page 139 Q14] A. The centre of gravity of the boy moves up and down in the vertical plane. Weight vector moves away from the base, as, in sitting position the mass distribution is different from that compared to the mass distribution when the boy is standing. Q3. Explain why a long pole is more beneficial to the tight rope walker if the pole has slight bending. [Refer to TB page 139 Q11] A. Two principles of physics contribute to a funambulist’s stability: i. The pole increases the funambulist’s moment of inertia. ii. The downward bend of the pole lowers the funambulist’s centre of gravity. iii. When an artist finds that he is falling towards left, he shifts the pole towards right, so that his centre of gravity stay undisturbed. Q4. Why is it easier to carry the same amount of water in two buckets, one in each hand than in a single bucket? [Refer to TB page 139 Q12] A. It is because in the later case centre of gravity of our body shifts towards the bucket and the there is a tendency that the line joining the centre of gravity and centre of equilibrium may fall outside our feet. However in the former case the centre of gravity not only gets lowered, but also it is at such a point that the line joining the centre of gravity and centre of equilibrium falls within our feet. Hence one bucket in each hand gives a stable equilibrium. SESSION 3. CENTRE OF GRAVITY 50

—— CCE Based Practice Questions —— AS1-Conceptual Understanding Very Short Answer Type Questions 1. State true or false. [Refer to Session 8.2 ] (i) Gravitational constant was found by Henry Cavendish. [ ] ] (ii) The value of ‘g’ decreases as we go upwards from the earth’s surface. ] [ (iii) We can calculate the speed of the moon using the equation V = 44R . 7T [ (iv) S.I. unit of weight is Newton. [] (v) Laws of gravitation are not applicable to point masses. [] (vi) Weight of a body and mass of a body is same in all cases. [ ] 2. Fill in the blanks. [Refer to Session 8.2 ] (i) All the bodies have the same acceleration equal to near the surface of the earth. (ii) If the distance between two bodies is doubled, the force of attraction, F, between them will be . (iii) The value of the universal gravitational constant is . (iv) According to the the sun is at centre and planets move around it. (v) The force with which a body is attracted by the earth is called its . CHAPTER 8. GRAVITATION 51

(vi) The mass of the earth is . (vii) A cricket ball is thrown vertically upwards with a initial velocity of 40 m/s. If g = 10 m/s2 the maximum height reached by the ball is . (viii) SI unit of weight is . (ix) In the formula F = G M1 M2 , G stands for the ____________________________. d2 3. State true or false. [Refer to Session 8.3 ] ] (i) A boy sitting on a chair can directly get up from the chair without any support. [ (ii) Centre of gravity always lies at the centre of an object. [] (iii) We cannot get up from a chair without bending our body. [] (iv) The centre of gravity of any freely suspended object lies directly beneath the point of suspension. [] (v) If the line through the centre of gravity falls outside the base then the object will not be stable. [] (vi) A body is in equilbrium when the weight vector goes through the base of the body. [] (vii) If the weight vector passes through the base of the body then the body will be in equilibrium. [] (viii) Centre of gravity is the point where total weight of the body acts. [ ] CHAPTER 8. GRAVITATION 52

(ix) Location of the centre of gravity is not important for stability. [ ] ] (x) Centre of gravity is simply the average position of weight distribution. [ 4. Fill in the blanks. . [Refer to Session 8.3 ] (i) The centre of gravity of a triangular lamina lies at its (ii) Centre of gravity of a circular ring lies at its . (iii) The simple method of locating the centre of gravity of an object is ______________ ________________________ . (iv) The downward bend of the pole lowers the centre of gravity. (v) The center of gravity of a uniform object, is at its . 5. Fill in the blanks. is a motion of the body with [Refer to Session 8.1 ] (i) a constant speed in circular path. (ii) is always directed towards the center of the circle during the uniform circular motion of a body. (iii) The force of attraction between two objects is called force. (iv) = gR (v) The net force required to maintain a body in uniform circular motion is known as . CHAPTER 8. GRAVITATION 53

(vi) The magnitude of centripetal force is given by . (vii) The net force which can change only the direction of the velocity of a body is called . (viii) The acceleration which causes changes in the direction of velocity of a body is called . (ix) Banking of roads provides the necessary_______________________________ . Short Answer Type Questions 6. Answer the following questions in 3-4 sentences. (i) [(Session 8.2)] What is free fall acceleration? (ii) [(Session 8.2)] What is the difference between mass and weight? (iii) [(Session 8.2)] A body is projected vertically up on a planet whose acceleration due to gravity is 8 m/s2 . What is the distance covered in its last second? 7. Answer the following questions in 3-4 sentences. (i) [(Session 8.3)] Define centre of gravity. (ii) [(Session 8.3)] What do you mean by stability? (iii) [(Session 8.3)] Where do the centres of gravity of a sphere and a triangular lamina lie? (iv) [(Session 8.3)] Why must you bend forward when carrying a heavy load on your back? 8. Answer the following questions in 3-4 sentences. (i) [(Session 8.1)] What is a force? (ii) [(Session 8.1)] What is centripetal acceleration? What is its direction? CHAPTER 8. GRAVITATION 54

Long Answer Type Questions 9. Answer the following questions in 6-8 sentences. (i) [(Session 8.2)] Explain the universal law of gravitation. (ii) [(Session 8.2)] Discuss the various factors on which the value of ‘g’ depends. 10. Answer the following questions in 6-8 sentences. (i) [(Session 8.1)] A ball thrown up vertically returns to the thrower after 6 sec. Find: a) The velocity with which it was thrown up. b) The maximum height it reaches. c) Its position after 4 s. AS2-Asking questions and making hypothesis Short Answer Type Questions 11. Answer the following questions in 3-4 sentences. (i) [(Session 8.2)] If there is an attractive force between all objects, why do we not feel ourselves gravitating towards massive buildings in our vicinity? 12. Answer the following questions in 3-4 sentences. (i) [(Session 8.3)] Can an object have more than one centre of gravity? Long Answer Type Questions 13. Answer the following questions in 6-8 sentences. (i) [(Session 8.2)] You buy a bag of sugar of weight ‘x’ at a place on the equator and take it to Antarctica. Would its weight be the same or does it vary? Why? AS3-Experimentation and field investigation Short Answer Type Questions 14. Answer the following questions in 3-4 sentences. (i) [(Session 8.3)] Write the standard equations when an object is dropped from a height. CHAPTER 8. GRAVITATION 55

Long Answer Type Questions 15. Answer the following questions in 6-8 sentences. (i) [(Session 8.2)] Describe an experiment to measure the weight of a freely falling body. What are the observations? AS4-Information skills and projects Short Answer Type Questions 16. Answer the following questions in 3-4 sentences. (i) [(Session 8.2)] Complete the table. S.No. M m R R2 F= GMm/R2 1 8 32 64 29 6 2G AS5-Communication through drawing and model making Long Answer Type Questions 17. Answer the following question. (i) [(Session 8.3)] Draw diagram to show the position of center of gravity in each of the following objects: a. Rectangular lamina b. Triangular lamina c. Ring AS6-Appreciation and aesthetic sense, Values Long Answer Type Questions 18. Answer the following questions in 6-8 sentences. (i) [(Session 8.3)] Explain why a small piece of stone is not attracted towards another big piece of stone on the earth’s surface. Also, the earth attracts an apple. Does the apple also attract the earth? If it does, why does the earth not move towards the apple? CHAPTER 8. GRAVITATION 56

AS7-Application to daily life, concern to bio diversity Short Answer Type Questions 19. Answer the following questions in 3-4 sentences. (i) [(Session 8.2)] Find out the weight of a freely falling ball which has a mass of 2 kg and is attracted by earth at 9.8 m/s2 . (ii) [(Session 8.2)] The mass of two freely moving asteroids are 2000 kg and 5000 kg respectively. The distance between these two asteroids is 5000 m. Find out the force of attraction between these two asteroids. (G = 7 × 10−11Nm2/kg2 ) 20. Answer the following questions in 3-4 sentences. (i) [(Session 8.3)] How can you get up from a chair without bending your body or legs? (ii) [(Session 8.3)] Write a short note on weightlessness. CHAPTER 8. GRAVITATION 57

Objective Questions AS1-Conceptual Understanding 21. Choose the correct answer. (i) Weight of 10 kg mass is equal to (B) 98 N (A) 9.8 N (C)980 N (D)1/9.8 N (ii) As we go from the equator to the poles, the value of ‘g’ (A) remains the same (B) decreases (C) increases (D)none of these (iii) All bodies whether large or small fall with the (A) same force (B) same acceleration due to gravity (C) same velocity (D)same momentum (iv) At which of the following locations is the value of ‘g’ the largest? (A) On top of Mount Everest (B) On top of Qutub Minar (C)At a place on the equator (D)A camp site in Antarctica (v) The force of gravitation between two bodies does not depend on (A) their separation (B) the product of their masses (C)the sum of their masses (D)gravitational constant AS2-Asking questions and making hypothesis 22. Choose the correct answer. (i) If the earth suddenly shrinks to half its present size, the value of acceleration due to gravity will CHAPTER 8. GRAVITATION 58

(A) become twice (B) remain unchanged (C)become half (D)become four times (ii) The weight of the body would not be zero (A) at the centre of the earth (B) during a free fall (C)in interplanetary space (D)on a frictionless surface AS3-Experimentation and field investigation 23. Choose the correct answer. (i) A stone dropped from the roof of a building takes 4 s to reach the ground. The height of the building is (A) 19.6 m (B) 39.2 m (C)156.8 m (D)78.4 m AS4-Information skills and projects 24. Choose the correct answer. (i) The earth attracts a body with a force of 10 N; with what force does that body attract the earth? (A) 10 N (B) 1 N (C)2 N (D)1/10 N (ii) A body is projected upwards with a velocity of 100 m/s. It will strike the ground in approximately (A) 10 s (B) 20 s (C)15 s (D)5 s CHAPTER 8. GRAVITATION 59

9. FLOATING BODIES SESSION 1 INTRODUCTION, DENSITY AND RELATIVE DENSITY 1.1 Mind Map 1.2 Terminology i. Density – Mass per unit volume. ii. Relative density – The ratio of the density of the object to density of water. iii. Lactometer – A device used to measure the relative density of milk. iv. Hydrometer – Device to measure the relative density of liquids. 1.3 Solved Examples Q1. Example 1: What is the effective density of the mixture of water and milk when (Refer to TB page 146) SESSION 1. INTRODUCTION, DENSITY AND RELATIVE DENSITY 60

i. they are taken with same masses. ii. they are taken with same volumes. A. Let us say the densities of water and milk are ρ1 and ρ2 . i) When they are taken with same mass ‘m’ and their volumes are V1 and V2 , the mass m m of water m = ρ1 V1 ; V1 = ρ1 and the mass of milk m = ρ2 V2 ; V2 = ρ2 Total mass of water and milk is m + m = 2m Total volume of water and milk is V1 + V2 = m + m =m 1 + 1 = m(ρρ11+ρ2ρ2) ρ1 ρ2 ρ1 ρ2 The effective density of the mixture (ρe f f )= T otal mass = 2m = T otal volume m(ρ1+ρ2)/ρ1 ρ2 2 ρ2 = 2ρρ11+ρρ22 (ρ1+ρ2)/ρ1 ii) When they are taken with same volume ‘V’ and their masses are m1 and m2 , the volume of water V = mρ11 That is m1 = Vρ1 and the volume of milk V = m2 ρ2 That is m2 = Vρ2 Total mass of water and milk is m1 + m2 = Vρ1 + Vρ2 = V (ρ1 + ρ2 ) Total volume of water and milk is V + V = 2V The effective density of the mixture (ρe f f ) = T otal mass T otal volume ρe f f = V (ρ1 +ρ2 ) = 1 (ρ1 + ρ2) 2V 2 1.4 Key Concepts i. We find some bodies float on water and some sink. ii. Objects which have a density less than the liquid in which they are kept, float on the surface of the liquid. iii. The relative density of a substance is the ratio of the density of the substance to the density of water. It is a ratio of similar quantities and has no unit. SESSION 1. INTRODUCTION, DENSITY AND RELATIVE DENSITY 61

1.5 Conceptual Understanding Q1. A solid sphere has a radius of 2 cm and a mass of 0.05 kg. What is the relative density of the sphere? [Refer to TB page 159 Q1] A. Radius = 2 cm Volume = 4 πr3 = 4 × 22 × 23 3 3 7 Mass = 0.05 kg = 50 g Density of sphere = Mass of solid = 50×3×7 = 1.49g/cc Volume of solid 4×22×8 Relative density of the sphere is also 1.49 as relative density is the ratio of densities of object to water and the density of water is 1 g/cc. Q2. A small bottle weighs 20 g when empty and 22 g when filled with water. When it is filled with oil, it weighs 21.76 g. What is the density of oil? [Refer to TB page 159 Q2] A. Weight of oil = 21.76 – 20 = 1.76 g Weight of water = 22 – 20 = 2 g Density = 1.76 = 0.88g/cm3 2 Q3. Explain density and relative density and write formulae. [Refer to TB page 159 Q5] A. Density is mass per unit volume mass. Density = Mass/ Volume. Units of density are g/cm3 or kg/cm3. Relative density is the ratio between the density of a substance and the density of wa- ter. To find the relative density of an object, we must first weigh the object and then weigh an equal volume of water. The two weights are then compared. So, relative density of an object = Density of an object/ Density of water. SESSION 1. INTRODUCTION, DENSITY AND RELATIVE DENSITY 62

Relative density is a ratio. So it has no units. Q4. What is the value of density of water? [Refer to TB page 159 Q6] A. Value of density of water in C.G.S system is 1 g/cm3 and in S.I system is 1000 kg/m3. Q5. Classify the following things into substances having Relative density > 1 and Relative density < 1. Wood, iron, rubber, plastic, glass, stone, cork, air, coal, ice, wax, paper, milk, kerosene, groundnut oil, soap. [Refer to TB page 159 Q8] A. i. Wood <1 ii. Iron >1 iii. Rubber <1 iv. Plastic <1 v. Glass >1 vi. Stone >1 vii. Cork <1 viii. Air <1 ix. Coal <1 x. Ice <1 xi. Wax <1 xii. Paper <1 xiii. Milk >1 xiv. Kerosene <1 xv. Groundnut oil <1 xvi. Soap >1 1.6 Asking Questions and Making Hypothesis Q1. Which is denser, water or milk? [Refer to TB page 159 Q9] A. Milk is denser than water. The density of water is 1.00 g/cm3 and the density of milk is about 1.03 g/cm3 . SESSION 1. INTRODUCTION, DENSITY AND RELATIVE DENSITY 63

1.7 Experimentation and Field Investigation Q1. Find the relative density of wood. Explain the process. [Refer to TB page 159 Q11] A. Relative density can be calculated directly by measuring the density of a sample and dividing it by the known density of the reference substance. The density of the sample is simply its mass divided by its volume. Although mass is easy to measure, the volume of an irregularly shaped sample can be more difficult to as certain. Aim: To find relative density of wood. Materials required: Overflow vessel, 50 ml measuring cylinder, spring balance, wooden block, water. Procedure: 1. Weigh the 50 ml measuring cylinder and note its weight. 2.Weigh the wooden block and note its weight. 3.Pour water in the overflow vessel until it starts dripping from its beak. 4.When water stops dripping from the beak, place the 50 ml measuring cylinder under it. 5.Slip the wooden block gently into the overflow vessel, ensuring that the water does not splash out. 6. Once the wooden block is in the overflow vessel, water flows out of the beak and collects in the 50 ml cylinder. 7. Wait till the flow of water from beak, stops. 8.Weigh the cylinder with the water that overflowed and record the weight. Relative density of wood=Weight of the wood/Weight of water equal to the volume of the wooden block. S.No. Weight of the Weight of the Weight of Weight of the Relative wooden block cylinder displaced water water displaced density of the and cylinder by the wooden wooden block block SESSION 1. INTRODUCTION, DENSITY AND RELATIVE DENSITY 64

Q2. How can you find the relative density of a liquid. [Refer to TB page 159 Q12] A. Aim: To find the relative density of a liquid. Material required: Small bottle of 50ml capacity (the bottle should weigh not less than 10gm), spring balance, any liquid (milk or oil or kerosene) about 50ml. Procedure: 1. Find the weight of empty 50ml bottle. 2. Fill the bottle with water and weigh it. 3. Find the weight of 50 ml water. 4. Replace the water with milk(or any other liquid) in the bottle. 5. Weigh the bottle with liquid. 6. Weight of 50ml liquid=Weight of bottle with liquid -Weight of empty bottle 7. Relative density of liquid = Weight of the liquid/ Weight of same volume of water S.No. Name Weight Weight Weight Weight Weight Relative of the of of of density liquid empty bottle water of botte of of liquid bottles with with liquid water liquid Q3. Find the relative density of different fruits and vegetables and write a list. [Refer to TB page 159 Q13] SESSION 1. INTRODUCTION, DENSITY AND RELATIVE DENSITY 65

A. S. No. Fruit/ vegetable Relative density 1 Custard Apple 0.650 2 Banana 1.14 3 Almonds 1.16 4 Pomegranate 0.920 5 Grapes 1.044 6 Cabbage 0.36 7 Potato 0.67 8 Onion 0.59 9 Chilli 0.29 10 Cauliflower 0.26 11 Apple 1.22 1.7 Information Skills and Projects Q1. You found the relative densities of some solids and some liquids by some activities. List the solids and liquids in increasing order of relative density. [Refer to TB page 160 Q4, Try These] A. List of solids in increasing order of relative density: Rubber ball, plastic cube, wood, plastic pen, rubber eraser, glass marble, iron nail, ge- ometry box. List of liquids in increasing order of relative density: Groundnut oil, Kerosene, Milk. SESSION 1. INTRODUCTION, DENSITY AND RELATIVE DENSITY 66

1.9 Communication Through Drawing and Model Making Q1. Make a lactometer with refill. What do you do to make the refill stand vertically straight? [Refer to TB page 159 Q14] A. Take an empty ball pen refill. It should have a metal point. Take a boiling tube and fill it with water. Use the pen to mark the point on the refill to show the part which is above the water surface. Pour out the water from the boiling tube and fill it with the milk. Float the refill in the milk. Put the second mark on the refill, at the point showing the part that is above the surface of the milk. Now pour a mixture of milk and water in the boiling tube. When we put the refill in the boiling tube, we find that the point is above the point made when refill is kept in milk. By using this method, we can find whether water is added in the milk or not. Refill is made to stand vertically by placing a cork which contains a small hole which can hold the refill. SESSION 1. INTRODUCTION, DENSITY AND RELATIVE DENSITY 67

SESSION 2 WHEN DO OBJECTS FLOAT ON WATER AND ATMOSPHERIC PRESSURE 2.1 Mind Map SESSION 2. WHEN DO OBJECTS FLOAT ON WATER AND ATMOSPHERIC ... 68

SESSION 2. WHEN DO OBJECTS FLOAT ON WATER AND ATMOSPHERIC ... 69

2.2 Terminology i. Atmospheric pressure – The pressure exerted by the atmosphere. ii. Barometer –The device to measure atmospheric pressure. 2.3 Key Concepts i. On all the objects floating in liquids an upward force called force of ‘buoyancy’ acts. ii. An object immersed in a fluid appears to have lost some weight. iii. This apparent loss of weight of an object immersed in a liquid is equal to the weight of displaced liquid. This is known as Archimedes’ principle. iv. When an object floats on the surface of a liquid, it displaces liquid having weight equal to its own weight. v. Force acting on unit area of the surface of an object is called pressure. vi. Atmospheric pressure = ρhg, where h = height of atmosphere, ρ= average density of atmosphere, g = acceleration due to gravity. vii. The pressure exerted by a liquid increases with depth below the surface of liquid. 2.4 Conceptual Understanding Q1. An ice cube floats on the surface of a glass of water (density of ice = 0.9 g/cm3 ). When the ice melts will the water level in the glass rise? [Refer to TB page 159 Q3] A. No. The level of water does not raise as the volume of the water ice mixture remains same when the ice melts. Q2. The volume of 50 g of a substance is 20 cm3. If the density of water is 1 g/cm3, will the substance sink or float when placed on the surface of water? What will be the mass of water displaced by the substance? [Refer to TB page 160 Q1, Try These] A. Let us compare the densities of the substance and that of water. Density of substance = mass volume Mass of substance = 50 g ; volume = 20 cm3 Density = 50 = 2.5 g/cm3 20 Density of water = 1 g/cm3 (i) Since the density of substance is greater than that of water the substance sinks in water. SESSION 2. WHEN DO OBJECTS FLOAT ON WATER AND ATMOSPHERIC ... 70

(ii) The volume of water displaced = volume of substance placed in water = 20 cm3 (iii) Density of water 1 g/cm3. Mass of water displaced = volume of the immersed object x density of the liquid in which the object is immersed = 20 x 1 g = 20 g Q3. Find the pressure at a depth of 10 m in water if the atmospheric pressure is 100 kPa. [1 Pa = 1 N/m2 ] [100 kPa = 105 Pa = 105 N/m2 = 1 atm] [Refer to TB page 160 Q2, Try These] A. Depth 'h' = 10 m; Atmospheric Pressure = 100 kPa Density of water = 1kg/m3 Pressure at depth 'h' is P = Atmospheric pressure + hρg = 100 + 10 x 1 x 9.8 = 100 + 98 = 198 kPa Q4. Why some objects float on water and some sink? [Refer to TB page 159 Q4] A. Floating or sinking of an object on water depends on two factors. a. Relative density. b. Weight of the water displace by the object. If the relative density of an object is greater than 1, the object sinks otherwise it floats. Even though the relative density is greater than 1, if the weight of the water dis- placed by the object equal to the weight of the object itself, the object floats on the water. SESSION 2. WHEN DO OBJECTS FLOAT ON WATER AND ATMOSPHERIC ... 71

2.5 Communication Through Drawing and Model Making Q1. Draw the diagram of mercury barometer. [Refer to TB page 159 Q15] A. SESSION 2. WHEN DO OBJECTS FLOAT ON WATER AND ATMOSPHERIC ... 72

SESSION 3 MEASURING THE FORCE OF BUOYANCY 3.1 Mind Map 3.2 Terminology i. Buoyancy –The upward force that a fluid exerts on an object less denser than itself. 3.3 Key Concepts i. The pressure exerted by a liquid increases with depth below the surface of liquid. ii. Pascal’s principle: It states that the external pressure applied to an enclosed volume of fluid is transmitted equally in all directions throughout the volume of the fluid. 3.4 Conceptual Understanding 73 SESSION 3. MEASURING THE FORCE OF BUOYANCY

Q1. What is buoyancy? [Refer to TB page 159 Q7] A. i. When an object is kept in a fluid, it experiences an upward force. ii. Substances thus appear lighter when immersed completely or partially in a liquid. iii. The tendency of a fluid to exert an upward force on the object wholly or partially im- mersed in it is called buoyancy. The upward force that acts on the object immersed in a fluid is called buoyant force. 3.5 Asking Questions and Making Hypothesis Q1. Iron sinks in water, wood floats in water. If we tied an iron piece to the same volume of wood piece, and dropped them in water, will it sink or float? Make a guess and find out whether your guess is correct or wrong with an experiment. Give reasons. [Refer to TB page 159 Q10] A. If we tied an iron piece to the same volume of wood piece, and dropped them in water, it sinks in water. Reason: The combined mass of the system increases, so the combined density also increases. Hence the body sinks in water. 3.6 Experimentation and Field Investigation Q1. Can you make iron float on water? How? [Refer to TB page 160 Q3, Try These] A. Any object will float on water as long as the mass of the water it displaces is more than or equal to the mass of the object. Objects built using materials that are more dense than water can still be made to float by making them hollow like a boat. 3.7 Information Skills and Projects Q1. Air brakes in automobiles work on Pascal’s principle. What about air brakes? Collect the information about the working process of air brakes. [Refer to TB page 160 Q5, Try These] A. Liquids and gases which have the property of same Pascal’s principle applies to air, a fluid and the pressure caused at a point in the air (fluid) at rest is transmitted equally in all directions throughout the air and this is the principle under which the air brakes work. SESSION 3. MEASURING THE FORCE OF BUOYANCY 74

3.8 Appreciation and Aesthetic Sense, Values Q1. How can you appreciate the technology of making ships float, using the material which sink in water. [Refer to TB page 159 Q16] A. Archimedes solved a problem: He noticed that as he lowered himself into the bath, the water displaced by his body overflowed the sides and he realized that there was a relationship between his weight and the volume of water displaced. This helped him solve the problem given to him by the king, as to whether his crown was made of pure gold or partly silver. Archimedes reasoned that if the crown had any silver in it, it would take up more space than a pure gold crown of the same weight because silver is not as dense as gold. He compared the crown’s volume with the volume of equal weights of gold and then silver, he found the answer that the crown was not pure gold. The Buoyancy Principle: Archimedes continued to do more experiments and came up with a buoyancy principle, that a ship will float when the weight of the water it displaces equals the weight of the ship and anything will float if it is shaped to displace its own weight of water before it reaches the point where it will submerge. It involves very sharp scientific calculations and engineering technologies. Really such type of technologies are highly appreciable. Q2. Write a note on Pascal’s discovery in helping to make hydraulic jacks? [Refer to TB page 160 Q17] A. A hydraulic jack’s functioning is described very accurately by Pascal’s principle, which states that a force applied to an enclosed fluid is transferred equally throughout the entire fluid. This means that the fluid must not be able to be compressed. When the jack’s pump is activated, it applies pressure on the hydraulic fluid, which fills the cylinder. Because the cylinder is completely filled while the pump is active and the one–way valve completely encloses the fluid, pressure builds within the cylinder. The pressure escapes via the easiest way possible – it pushes up on the plate of the jack, hence putting out force. The pump basically exerts a small force on the fluid continuously until the fluid has enough pressure to push up the jack, which lifts whatever is being lifted at the time. This means that the hydraulic jack can exert massive force with simply a pump. Pascal’s discovery is one of the most important milestones in the history of science. SESSION 3. MEASURING THE FORCE OF BUOYANCY 75

Hydraulic jacks are used not only in automobile work shops but in many industries where heavy weights are to be lifted with a little force. Q3. Write a note on Archimedes discovery of force of buoyancy? [Refer to TB page 160 Q18] A. According to Archimedes’ principle, “Any object, wholly or partly immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by it”. The weight of the displaced fluid is directly proportional to the volume of the displaced fluid (if the surrounding fluid is of uniform density). Thus, among completely submerged objects with equal masses, objects with greater volume have greater buoyancy. The principle has great application in science and technology. Archimedes’ Principle of buoyancy is applied in our daily life in many ways. Fish, human, swimmers, ice bergs and ships float follow Archimedes’ principle of buoyancy. Rise of balloon in air also follows Archimedes’ principle. 3.9 Application to Daily Life, Concern to Bio Diversity Q1. Where do you observe Archimedes’ principle in our daily life? Give two examples. [Refer to TB page 160 Q19] A. i) Construction of ships. ii) Hot air balloons. Q2. Where do you observe Pascal’s principle in our daily life? Give a few examples. [Refer to TB page 160 Q20] A. i) Hydraulic jacks ii) Hydraulic brakes iii) Hydraulic pumps iv) Hydraulic cranes v) Siphons SESSION 3. MEASURING THE FORCE OF BUOYANCY 76

—— CCE Based Practice Questions —— AS1-Conceptual Understanding Very Short Answer Type Questions 1. State true or false. [Refer to Session 9.1 ] (i) Milk is denser than water. [] (ii) If we throw a glass marble and a wooden block in water, the wooden block sinks as it has higher density than water. [] (iii) The relative density of a substance is the ratio of the density of the substance to the density of water. [] (iv) We cannot use hydrometer to find the density of any liquid. [ ] (v) Value of density of water in C. G. S system is 1 g/cm3. [ ] 2. Match the following. Column B [(Session 9.1)] Column A [] a. = Density of an object Density of water i. Density ii. Relative density of an object [ ] b. = Mass Volume iii. Relative density of a liquid [] c. = kg iv. Unit of density [] m3 d. = 1 (ρ1 + ρ2 ) 2 v. Effective density of the mixture [ ] e. = Weight of the liquid Weight of the same volume of water CHAPTER 9. FLOATING BODIES 77

3. State true or false. [Refer to Session 9.3 ] (i) The density of salt water is greater than that of fresh water. [ ] (ii) Hydraulic brakes are used in cars. [] (iii) Hydraulic jacks are used for lifting automobiles in workshops. [ ] (iv) We cannot use Archimedes’ principle in construction of ships. [ ] (v) Any object, wholly or partly immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by it. [] 4. Match the following. Column B [(Session 9.3)] [ ] a. Lactometer Column A i. Bramah press ii. Density of mercury in S.I. system [ ] b. Barometer iii. Instrument used to measure [ ] c. 13.6 x 103 kg/m3 atmospheric pressure iv. Instrument used to measure purity [ ] d. Hydraulic jack of milk v. Device used to lift a car [ ] e. Application of Pascal’s principle CHAPTER 9. FLOATING BODIES 78

5. Fill in the blanks. [Refer to Session 9.3 ] (i) Apparent loss of weight must be equal to the _____________________________. (ii) used buoyancy principle to know the purity of gold crown. (iii) A hydraulic jack’s functioning is described very accurately by principle. (iv) If is applied to an enclosed volume of fluid, it is transmitted equally in all directions throughout the fluid volume. 6. State true or false. [Refer to Session 9.2 ] (i) The pressure exerted by a liquid increases with depth below the surface of liquid. [] (ii) Pressure is the thrust per unit area of a surface. [] (iii) An object immersed in a fluid appears to have gained some weight. ] [ (iv) The density of salt water is lesser than that of fresh water. [ ] (v) Certain objects float on water because their density is less than the density of water. [] CHAPTER 9. FLOATING BODIES 79

Short Answer Type Questions 7. Answer the following questions in 3-4 sentences. (i) [(Session 9.1)] How is the relative density of liquids obtained? (ii) [(Session 9.1)] Write the formulae for: a) Density, b) Relative density of an object, and c) Relative density of a liquid. (iii) [(Session 9.1)] A ball has a radius of 4 cm and mass of 1 kg. What is the relative density of the ball? 8. Answer the following questions in 3-4 sentences. (i) [(Session 9.3)] State Archimedes’ principle. (ii) [(Session 9.3)] How do hydraulic pumps work? 9. Answer the following questions in 3-4 sentences. (i) [(Session 9.2)] Define 1 Pascal. (ii) [(Session 9.2)] What happens if we place a block of wood in kerosene oil? Explain the observation. (iii) [(Session 9.2)] A dead body floats on water with its head immersed in water. Explain. Long Answer Type Questions 10. Answer the following questions in 6-8 sentences. (i) [(Session 9.3)] What do you mean by buoyancy? In which direction does the buoyant force acts on an object immersed in a liquid act? 11. Answer the following questions in 6-8 sentences. (i) [(Session 9.2)] What happens if we use any liquid other than mercury in a barometer? CHAPTER 9. FLOATING BODIES 80

AS2-Asking questions and making hypothesis Short Answer Type Questions 12. Answer the following questions in 3-4 sentences. (i) [(Session 9.1)] Find out the effective density of a mixture of water and milk when they are taken in equal volumes. AS3-Experimentation and field investigation Short Answer Type Questions 13. Answer the following questions in 3-4 sentences. (i) [(Session 9.1)] An oil bottle weighs 30 g. After removing the oil, the bottle weighed 10 g. When it is filled with water the bottle weighs 28 g. Now find the density of oil. (ii) [(Session 9.1)] What is a lactometer? Draw the diagram of an improvised lactometer. Name any two similar instruments which can be used to find the density of any liquid. 14. Answer the following questions in 3-4 sentences. (i) [(Session 9.3)] List the factors affecting buoyant force. Long Answer Type Questions 15. Answer the following questions in 6-8 sentences. (i) [(Session 9.2)] Describe a simple activity to show that a body loses weight when immersed in a fluid. CHAPTER 9. FLOATING BODIES 81

AS4-Information skills and projects Long Answer Type Questions 16. Answer the following questions in 6-8 sentences. (i) [(Session 9.1)] The densities of some substances are given: Substance Density (kg/m3 ) Lead 11,500 Aluminium 2700 Water 1000 Gold 19300 Mercury 13600 Iron 8000 Answer the following questions: a) Arrange the substances in the increasing order of their relative densities. b) What will be the mass of lead brick with dimensions of 5 cm x 10 cm x 20 cm? c) What is the relative density of aluminium? d) If the mass of iron block is 640 kg, find the volume of iron. AS5-Communication through drawing and model making Short Answer Type Questions 17. Answer the following question. (i) [(Session 9.2)] Draw the image of a barometer. CHAPTER 9. FLOATING BODIES 82

AS6-Appreciation and aesthetic sense, Values Short Answer Type Questions 18. Answer the following questions in 3-4 sentences. (i) [(Session 9.2)] Why do we use hydrometer and barometer? AS7-Application to daily life, concern to bio diversity Short Answer Type Questions 19. Answer the following questions in 3-4 sentences. (i) [(Session 9.3)] It is easier for a man to swim in sea water than in river water. Why? CHAPTER 9. FLOATING BODIES 83

Objective Questions (B) iron nail AS1-Conceptual Understanding (D)copper plate 20. Choose the correct answer. (i) An object that floats on water is (A) cork (C)rupee coin (ii) Buoyant force depends on (B) density of liquid (A) weight of fluid displaced (D)all of these (C)accleration due to gravity (iii) By the condition of floatation, if d1 and d2 are the densities of liquids in which a hydrometer sinks to depths of h1 and h2 respectively, which of the following is true? (A) d1 = h1 d2 h2 (B) d1 = h2 d2 h1 (C)d1 h2 = d2 h1 (D)None of the above (iv) Loss in weight is more in (A) salted water (B) tap water (C)same in both (D)double in salt water than tap water CHAPTER 9. FLOATING BODIES 84

(v) The upward force applied on an object immersed in a liquid is called (A) friction (B) atmospheric pressure (C) buoyancy (D)repulsive force (vi) A balloon filled with hydrogen gas rises up into the air due to the (A) weight of the balloon (B) low density of the air (C)high density of the air (D)buoyant force exerted on it by air (vii) Atmospheric pressure in terms of height of mercury column (in cm) is (A) 76 (B) 67 (C) 760 (D) 7.6 (viii) Which of the following principle says that weight of liquid displaced and upthrust are equal? (A) Pascal’s principle (B) Faraday’s principle (C)Archimedes’ principle (D)Charles’s principle (ix) Unit of pressure in the S.I. system is (B) Pascal (A) Torricelli (C) Henry (D) Ampere (x) Bramah press applies __________ principle. CHAPTER 9. FLOATING BODIES 85

(A) Pascal’s (B) Faraday’s (C) Archimedes’ (D) Charles’s (xi) The correct increasing order of relative densities is: (A) Air >water >iron (B) Water >iron >air (C)Water >iron <air (D)Air <water <iron (xii) The principle on which the hydrometer works is (A) Bernoulli’s principle (B) Pascal’s principle (C)Archimedes’ principle (D)Buoyancy principle (xiii) ’ρ ’ in the formula for calculating the pressure difference between two levels in a liquid denotes (A) pressure (B) volume (C)relative density (D) density AS3-Experimentation and field investigation 21. Choose the correct answer. (i) _____________ is used to determine the purity of a sample of milk. (A) Barometer (B) Lactometer (C) Thermometer (D) Hygrometer AS4-Information skills and projects (B) 13.6 × 103kg/m3 (D) 13.6kg/cc 22. Choose the correct answer. (i) Density of mercury in SI system is (A) 13.6 × 102gram/cc (C)13.6 × 102gram/cc CHAPTER 9. FLOATING BODIES 86

AS6-Appreciation and aesthetic sense, Values 23. Choose the correct answer. (i) Scientist who gave the principle about what happens when an external pressure is applied to an enclosed liquid is (A) Newton (B) Galileo (C) Pascal (D) Einstein CHAPTER 9. FLOATING BODIES 87

10. WORK AND ENERGY SESSION 1 WORK 1.1 Mind Map 1.2 Terminology i. Work – Product of force and displacement. 1.3 Solved Examples Q1. Example 1: A boy pushes a book kept on a table by applying a force of 4.5 N. Find the work done by the force if the book is displaced through 30 cm along the direction of push.( Refer to TB page 165) A. Force applied on the book (F) = 4.5 N SESSION 1. WORK 88

Displacement (s) = 30 cm = = 30 m = 0.3 m 100 Work done, W = F s = 4.5 × 0.3 = 1.35 J Q2. Example 2: Calculate the work done by a student in lifting a 0.5 kg book from the ground and keeping it on a shelf of 1.5 m height. (g = 9.8 m/s2 ) ( Refer to TB page 165) A. The mass of the book = 0.5 kg The force of gravity acting on the book is equal to ‘mg’ That is mg = 0.5 x 9.8 = 4.9 N The student has to apply a force equal to that of force of gravity acting on the book in order to lift it. Thus force applied by the student on the book, F = 4.9 N Displacement in the direction of force, s = 1.5 m Work done, W = F s = 4.9 x 1.5 = 7.35 J Q3. Example 3: A box is pushed through a distance of 4 m across a floor offering 100 N resistance. How much work is done by the resisting force? ( Refer to TB page 166 ) A. The force of friction acting on the box, F = 100 N The displacement of the box, s = 4 m The force and displacement are in opposite directions. Hence work done on the box is negative. That is, W = – F s = – 100 x 4 = – 400 J Q4. Example 4: A ball of mass 0.5 kg thrown upwards reaches a maximum height of 5 m. Calculate the work done by the force of gravity during this vertical displacement considering the value of g = 10 m/s2. ( Refer to TB page 167 ) SESSION 1. WORK 89

A. Force of gravity acting on the ball, F = mg = 0.5 x 10 = 5 N Displacement of the ball, s = 5 m The force and displacement are in opposite directions. Hence work done by the force of gravity on the ball is negative. W = – F s = – 5 x 5 = – 25 J 1.4 Key Concepts i. If a force acting on a body (F) causes a displacement (s) or produces change in the position of body, then work (W) is said to be done. ii. The amount of work done, W = F x s. iii. The formula W = F x s can be used only in case only in translatory motion. iv. Work is a scalar because it has only magnitude but no direction. v. The work done by a force is considered as negative if the force acting on the object and displacement are in opposite directions. vi. If the work has positive value, the body on which work has been done would gain energy. If work has negative value, the body on which work has been done loses energy. 1.5 Conceptual Understanding Q1. Define work and write its units. [Refer to TB page 181 Q1] A. (i) Work: The work done is equal to the product of the force and the displacement. Work done = Force x Displacement W=Fxs (ii) Unit of work = newton –meter (Nm) (or) joule (J) SESSION 1. WORK 90

Q2. Give a few examples where displacement of an object is in the direction opposite to the force acting on the object. [Refer to TB page 181 Q2] A. Examples where displacement of an object is in the direction opposite to the force acting on the object: i. When a ball is thrown up, the motion is in the upward direction, whereas the force due to earth’s gravity is in the downward direction. ii. A rubber ball moving on a plane ground will come to stop after sometime due to frictional force acting on it in opposite direction. Q3. A cycle together with its rider weighs 100 kg. How much work is needed to set it moving at 3 m/s [Refer to TB page 183 Q3, Try These] A. Mass of cycle together with cycle (m) = 100 kg Velocity (v) = 3 m/s Kinetic energy, K.E = ½ mv2 =1/2 x 100 x (3)2 = 450 J Work done by the rider of cycle = 450 J Q4. A man with a box on his head is climbing up a ladder. The work done by the man on the box is [Refer to TB page 182 Q15] (A) Positive (B) Negative (C) Zero (D) Undefined A. (A) Positive Q5. A porter with a suitcase on his head is climbing up a flight of stairs with uniform speed. The work done by the “weight of the suitcase” on the suitcase is [Refer to TB page 182 Q16] (a) Positive (b) Negative SESSION 1. WORK 91

(c) Zero (d) Undefined A. (b) Negative 1.6 Asking Questions and Making Hypothesis Q1. Let us assume that you have lifted a suitcase and kept it on a table. On which of the following does the work done by you depend or not depend? Why? [Refer to TB page 183 Q4, Try These] i. The path taken by the suitcase. ii. The time taken by you in doing so. iii. The weight of the suitcase. iv. Your weight. A. i. The path taken by the suitcase: Doesn’t depend because the height from the ground to the top of the table is fixed in this case. ii. The time taken by you in doing so: It does not depend on the time taken because the work done is same. If you take less time your power will be more otherwise power will be less. iii. The weight of the suitcase: It depends on the weight of the suitcase because as the weight of the suitcase increases, the work done will also increase. iv. Your weight: The work done does not depend on your weight. 1.7 Application to Daily Life, Concern to Bio Diversity Q1. Why does a person standing for a long time get tired when he does not appear as doing any work? [Refer to TB page 182 Q19] A. i. A person standing for a long time get tired though he does not appear as doing any work externally. ii. But many works are being done inside the body. The muscles of legs become stretched when he stands for a long time. iii. His heart has pumped more blood to muscles. These actions of the body lead to loss of energy inside the body and so he gets tired. iv. This happens due to the utilization of energy produced in his body. SESSION 1. WORK 92

SESSION 2 ENERGY 2.1 Mind Map 2.2 Terminology i. Transfer of energy – Energy transfer is the conveyance of energy from one item to another or the conversion of one form of energy into another; the transfer occurs among different scales and motions. ii. Sources of energy – Sources from which energy can be obtained to provide heat, light, and power. iii. Kinetic energy – The energy possessed by a body by virtue of its motion is called kinetic energy. iv. Potential energy – The energy possessed by a body by virtue of its position or state is called potential energy. SESSION 2. ENERGY 93

v. Mechanical energy – Mechanical energy is the sum of kinetic energy and potential energy. 2.3 Solved Examples Q1. Example 5: Find the kinetic energy of a ball of 250 g mass, moving at a velocity of 40 cm/s. (Refer to TB page 172 ) A. Mass of the ball, m = 250 g = 0.25 kg Speed of the ball, v = 40 cm/s = 0.4 m/s Kinetic Energy, K.E. = 1 (0.25) x (0.4)2 = 0.02 J 2 Q2. Example 6: The mass of a cyclist together with the bicycle is 90 kg. Calculate the work done by cyclist if the speed increases from 6 km/h to 12 km/h. ( Refer to TB page 172 ) A. Mass of cyclist together with bike, m = 90 kg Initial velocity, u = 6 km/h = 6 x 5 = 5 m/s 18 3 Final velocity, v = 12 km /h = 12 x 5 = 10 m/s 18 3 Initial kinetic energy, K.E.i = 1 mu2 2 = 1 (90) 5 2 2 3 = 125 J Final kinetic energy, K.E. f = 1 mv2 2 = 1 (90) 10 2 2 3 = 1 × (90) × 10 × 10 2 3 3 = 500 J The work done by the cyclist = Change in kinetic energy = K.E. f – K.E.i = 500 J – 125 J = 375 J SESSION 2. ENERGY 94

Q3. Example 7: A block of 2 kg is lifted up through 2 m from the ground. Calculate the potential energy of the block at that point. [Take g = 9.8m/s2 ] (Refer to TB page 175) A. Mass of the block, m = 2 kg Height raised, h = 2 m Acceleration due to gravity, g = 9.8 m/s2 Potential energy of the block, P.E. = m g h = 2 × 9.8 × 2 = 39.2 J Q4. Example 8: A book of mass 1 kg is raised through a height ‘h’. If the potential energy increased by 49 J, find the height raised.( Refer to TB page 175 ) A. The increase in potential energy = mgh That is, mgh = 49 J i.e., 1 × 9.8 × h = 49 J The height raised, h = 49 =5m 1×9.8 2.4 Key Concepts i. Energy is defined as the capacity to do work. The energy depends on position and state of the object which is doing work. ii. Whenever work has been done on an object its energy either increases or decreases. iii. The energy possessed by a body by virtue of its motion is called kinetic energy. iv. The energy possessed by a body by virtue of its position or state is called potential energy. v. Mechanical energy is the sum of kinetic energy and potential energy. 2.5 Conceptual Understanding 95 Q1. What is mechanical energy? [Refer to TB page 181 Q4] SESSION 2. ENERGY

A. The sum of the kinetic energy and the potential energy of an object is called its mechan- ical energy. Q2. One person says that potential energy of a particular book kept in an almirah is 20 J and other says it is 30 J. Is one of them necessarily wrong? Give reasons. [Refer to TB page 183 Q1, Try These] A. i. Yes. One of them is necessarily wrong because both of them are considering the same book which is kept in an almirah at the same position. ii. As the potential energy P.E. = mgh, the mass of book and height at which is kept (h) and g at a place are all identical. So potential energy also should be the same. Q3. What is potential energy? Derive an equation for gravitational potential energy of a body of mass ‘m’ at a height ‘h’. [Refer to TB page 181 Q7] A. Potential energy: The energy possessed by an object because of its position or shape is called its potential energy. i. Consider an object of mass ‘m’. ii. Let it be raised through a height, ‘h’ from the ground. iii. The minimum force required to raise the object, is equal to the weight of the object, viz., mg. iv. The object gains energy equal to the work done on the object against gravity i.e.; work done w = force × displacement = mg × h Therefore, Potential energy = mgh Q4. What is kinetic energy? Derive the equation for the kinetic energy of a body of mass ‘m’ moving at a speed ‘v’. [Refer to TB page 181 Q8] A. Kinetic Energy: The energy possessed by a body due to its motion is called Kinetic energy. Consider an object of mass ‘m’ moving at a speed ‘v’.Let it be displaced through a distance ‘s’ when a constant force ‘F’ acts on it in the direction of its displacement. Now the work done W = F × s SESSION 2. ENERGY 96

The work done on the object will cause a change in its speed from ‘u’ to say ‘v’. Let ‘a’ be the acceleration produced. From the equation of motion : v2 – u2 = 2 a s We have s = (v2 – u2 ) / 2a We know F = ma So the work done by the force F is w = ma × (v2 – u2 ) / 2a If the object is starting from rest, u = 0 Then w = ½ m v2 It is clear that the work done is equal to the change in the kinetic energy in the object. So, the kinetic energy possessed by an object of mass, ‘m’ and moving at a speed ‘v’ is K.E = ½ m v2. Q5. A free–fall object eventually stops on reaching the ground. What happens to its kinetic energy? [Refer to TB page 182 Q9] A. i. The potential energy of a freely falling object converts completely into kinetic en- ergy when it reaches the ground. ii. But this kinetic energy is completely transferred to the surface of the earth and so the body comes to rest. iii. Its kinetic energy becomes zero. Q6. A 10 kg ball is dropped from a height of 10 m. Find (a) the initial potential energy of the ball (b) the kinetic energy just before it reaches the ground and (c) the speed just before it reaches the ground. [Refer to TB page 183 Q2, Try These] A. (a) Potential energy of the body: m = mass of ball = 10 kg ; g = 9.8 m/s2 , height from which dropped (h) = 10 m. but P.E. = mgh Potential energy = 10 × 9.8 × 10 = 980 J (b) The potential energy is converted into kinetic energy as the body reaches the ground. K.E.= P.E. Kinetic energy before it reaches ground = 980 J. SESSION 2. ENERGY 97

(c) If ’v’ is the speed on reaching the ground, then Kinetic energy = ½ m v2 = 980 J m v2 = 1960 m = 10 kg, v2 = 1960/10 = 196 √ v = 196 = 14 Speed just before it reaches the ground = 14 m/s. Q7. Find the mass of a body which has 5 J of kinetic energy while moving at a speed of 2 m/s. [Refer to TB page 182 Q12] A. Kinetic energy of a body K.E.= ½ m v2 K.E. = 5 J; speed = 2 m/s mass of body (m) = ? K.E. = 5 = ½ m (2)2 m = 10 / 4 = 2.5 kg Mass of body = 2.5 kg. Q8. When the speed of a ball is doubled its kinetic energy [Refer to TB page 182 Q13] (A) Remains same (B) Gets doubled (C) Becomes half (D) Becomes 4 times A. (D) Becomes 4 times Reason: Speed originally be ‘v’ and mass of object be ‘m’. Now speed is doubled = present speed x 2 Now the K.E. is = m(2v)2 = 4 m v2 SESSION 2. ENERGY 98