Text Book Solutions All Class

Multiple Choice Questions

Q.1. Kerosene and Petrol are miscible liquids. The difference between their boiling points is more than 25°C. The two liquids can be separated from each other by _____. 
(a) Simple distillation
(b) Steam distillation
(c) Fractional distillation
(d) Any of these

Correct Answer is Option (a)
By simple distillation. Vapours of the liquid which has low boiling point will be formed first and collected. The liquid having higher boiling point will remain in the vessel.

Q.2. How can a saturated solution be made unsaturated?
(a) By heating the solution
(b) By cooling the solution
(c) By increasing the amount of solute
(d) By centrifugation of the solution

Correct Answer is Option (a)
A saturated solution can be made unsaturated by increasing the temperature of solution by heating it or by increasing the amount of solvent in the solution i.e. diluting it.

Q.3. The cause of Brownian movement is:
(a) Heat changes in liquid state
(b) Convection currents
(c) Impact of molecules of dispersion medium on on dispersed phase
(d) Attractive forces between the particles of dispersed phase and dispersion medium.

Correct Answer is Option (c)
Zig-zag path of colloidal particles is called Brownian Movement. Zig-zag path of particles is due to collision of particles of dispersed phase and dispersion medium.

Q.4. In which of the following, dispersed phase is a liquid and dispersion medium is a gas? 
(a) Cloud
(b) Smoke
(c) Gel
(d) Soap bubble

Correct Answer is Option (a)

• In a cloud, tiny water droplets are suspended in air.
• This makes it an example of a liquid dispersed phase in a gas dispersion medium.

Q.5. At room temperature, a non-metal which is a liquid is: 
(a) Sulphur
(a) Bromine
(a) Chlorine
(a) Nitrogen 

Correct Answer is Option (b)

Bromine is the only non-metal that exists in liquid form at room temperature. Here are some key points:

• It is a reddish-brown liquid.
• Bromine has a strong, unpleasant odour.
• It is used in various applications, including flame retardants and pesticides.

Fill in the Blanks

1. Common salt is _________.

Ans: Compound
Common salt, chemically known as sodium chloride (NaCl), is a compound formed from the chemical combination of sodium and chlorine.

2. A mixture contains more than ______ substance mixed in ______ proportion.

Ans:  One, any
A mixture is defined as a combination of two or more substances that can be present in any proportion.

3. Properties of a __________ are different from its constituent elements, whereas a _______

 shows the properties of its constituting elements.

Ans: Compound, mixture
A compound has distinct properties that differ from those of its individual elements, while a mixture retains the properties of its components.

4. A solution is defined as a mixture that is_________

Ans: Homogeneous
A homogeneous mixture has a uniform composition throughout, meaning the components are evenly distributed.

5. We can remove salts from a solution by using the process of _________

Ans: Evaporation
Evaporation is a method used to separate a solute from a solvent by heating the solution until the solvent turns into vapor.

6. A pure substance has a fixed__________ or ______ at constant temperature.

Ans: Melting Point, Boiling Point
A pure substance has specific melting and boiling points that do not change under constant temperature conditions.

7. An element is made up of only one kind of _________.

Ans: Atoms
Elements consist of only one type of atom, which defines their unique properties.

8. Miscible liquids are separated by ________ .

Ans: Fractional distillation
Fractional distillation is a technique used to separate miscible liquids based on their different boiling points.

 
9. Immiscible liquids are separated by using a _______.

Ans: Separating funnel
A separating funnel is used to separate immiscible liquids based on their different densities.

10. Filtered tea is a _________ mixture.

Ans: Homogeneous
Filtered tea is homogeneous because it has a uniform composition throughout after the solid tea leaves are removed.

11. Alloy is a _______.

Ans: Solid solution
An alloy is a solid solution of two or more metals, which results in improved properties compared to the individual metals.

12. Sublimation of camphor is a _________ change.

Ans: Physical
Sublimation is a physical change where a substance transitions directly from solid to gas without passing through the liquid state.

13. Most common chemical change we observe in our routine life is rusting of______.

Ans: Iron
Rusting is a chemical reaction that occurs when iron reacts with oxygen and moisture, forming iron oxide.

Very Short Answer Question 

Q.1. Classify the substances given in below figure into elements and compounds

Ans: 

Q.2. Give one example each of homogeneous and heterogeneous mixture.

Ans:  Homogeneous mixture: An example is brass, which is a uniform mixture of metals. Heterogeneous mixture: An example is sand and water, where the components remain distinct and easily separable.

Q.3. Name the apparatus by which mixture of oil and water can be separated.

Ans: Separating funnel is the apparatus used to separate a mixture of oil and water.

Q.4. Is brass a mixture or a compound?

Ans: Brass is classified as a mixture rather than a compound. This is due to the following reasons:

• Brass is made up of approximately 30% zinc and 70% copper.
• In a mixture, the individual components retain their own properties.
• Brass is a mixture because its composition can vary and its constituents retain their properties.

Q.5. What type of solution is an alloy? Liquid solution or solid solution

Ans: Alloy is a type of solid solution. Key points:

• An alloy consists of two or more metals or a metal and a non-metal.
• It cannot be separated into its components by physical methods.
• Alloys exhibit the properties of their constituent materials.
• For example, brass is made of approximately 30% zinc and 70% copper.

Q.6. A mixture consisting of two miscible liquids ‘A’ and ‘B’ whose boiling points differ by 50 C can be separated by which process?

Ans: Fractional distillation is the process used to separate a mixture of two miscible liquids, ‘A’ and ‘B’, when their boiling points differ by 50°C.

 
Q.7. Give one example of solid- liquid homogeneous mixture.

Ans:  Salt in water solution

Q.8. What is a Aqua regia?

Ans: Aqua regia is a highly-corrosive mixture of – nitric acid and hydrochloric acid. The mixture is formed by freshly mixing concentrated nitric acid and hydrochloric acid, usually in a volume ratio of 1:3

Q.9. Which method is used to separate two immiscible liquids?

Ans: Separating two immiscible liquids can be effectively achieved using a separating funnel.

• The separating funnel allows the two liquids to separate based on their density.
• Each liquid forms a distinct layer, making it easy to pour out one layer while leaving the other behind.
• This method is commonly used in laboratories for liquid-liquid extractions.

Q.10. Name two elements which are in liquid state at room temperature?

Ans: The only liquid elements at standard temperature and pressure arebromine (Br) and mercury (Hg). Although, elements caesium (Cs),rubidium (Rb), Francium (Fr) and Gallium (Ga) become liquid at or just above room temperature.

Short Answer Types QuestionsQ.1. Try segregating the things around you as pure substances or mixtures.

You can separate materials around you into pure substances or mixtures by performing simple experiments. Here’s how:

• Mix chalk powder with water.
• Observe that the chalk powder does not dissolve.
• Let the mixture settle; the chalk will form a layer at the bottom.
• Carefully pour off the water to separate the chalk.

This method demonstrates how mixtures can be separated into their individual components.

Q.2. What is meant by a substance? 

A substance is a type of matter that consists of particles that cannot be separated by any physical process. Key characteristics include:

• All particles have similar chemical properties.
• Substances can be classified as either elements or compounds.
• Elements cannot be broken down into simpler substances.
• Compounds consist of two or more different elements chemically combined.

In summary, a substance is a pure form of matter with consistent properties throughout.

Q.3. What type of mixtures are separated by the technique of crystallisation? 

From impure samples of solids, pure solid crystals can be obtained by the method of crystallization for eg to obtain pure sugar from impure sample of the same.

Q.4. What is tyndall effect? Which kinds of solution show it?

The Tyndall effect is the scattering of light by particles in a solution. This effect occurs when light passes through a medium containing small particles, making the path of the light visible. Solutions that exhibit the Tyndall effect include:

• Colloidal solutions: These contain particles that are larger than those in true solutions but smaller than those in suspensions.
• Examples: Milk and fog show the Tyndall effect due to their dispersed particles.

Q.5. What is centrifugation? Where it is used?

Centrifugation is a technique used to separate components of a mixture based on their density. It works by spinning the mixture rapidly, causing denser particles to settle at the bottom while lighter ones rise to the top.

• Commonly used to separate cream from milk.
• Also applied in laboratories for separating blood components.
• Used in various industries, including pharmaceuticals and biotechnology.

Q.6. What is crystallization? Where is it used? Why is this better than simple evaporation technique?

Crystallization is a process that separates a pure solid in the form of crystals from its solution. It is used to purify solids. For e.g. salt from sea water is purified using crystallization.
It is a better technique than simple evaporation because:
(a) Some solid may decompose or get charred on heating to dryness during evaporation.
(b) On evaporation, some of the impurities still remain dissolved in the solution.

Q.7. What is a colloid? What are its various properties?

Colloids are heterogeneous mixtures where the particles are too small to be seen with the naked eye. Their properties include:

• Heterogeneous mixture: Although they are heterogeneous, they often appear homogeneous.
• Particle size: The particles are too small to be individually visible.
• Tyndall effect: They scatter light, making the path of a beam visible.
• Stability: The particles do not settle when left undisturbed.

Q.8. Write a method to separate different gases from air.

Air is a homogeneous mixture of various gases. It can be separated into its components using fractional distillation. The process involves the following steps:

• Compress and cool the air by increasing pressure and decreasing temperature.
• This produces liquid air. Allow the liquid air to warm up slowly in a fractional distillation column.
• The gases will separate according to their boiling points at different heights in the column.

Q.9. Explain the following giving examples. 
(a) saturated solution 
(b) pure substance 
(c) colloid 
(d) suspension 

(a) saturated solution: It is a solution in which no more solute particles can be dissolved at a particular temperature.
(b) pure substance: Such substance that has a uniform composition i.e. has particles with identical properties is called pure substance eg sugar, salt, water, nitrogen etc.
(c) colloid: It is a kind of heterogeneous mixture/solution in which particle size is between 1nm and 1000nm. Colloids have dispersion medium and dispersed phase.eg smoke, milk, shaving cream, jelly, cheese etc.
(d) suspension: It is a kind of heterogeneous mixture in which insoluble solid particles remain suspended in the medium and dispersion particles are visible to the unaided eyes.eg muddy river water, chalk powder in water, dust storm, sand in water etc.

Q.10. Write the steps you would use for making tea. Use the words solution, solvent, solute, dissolve, soluble, insoluble, filtrate and residue.

To make tea, follow these steps:

• Start by heating a sufficient amount of solvent (water) in a pan.
• Once heated, add a small amount of solute (sugar) to the water. The sugar will dissolve completely, forming a true solution.
• Add tea leaves, which are insoluble, along with a soluble liquid (milk).
• Boil the mixture to enhance flavour.
• After boiling, use a sieve to filter the mixture. The liquid that passes through is the filtrate, which is your tea.
• The leftover tea leaves in the sieve are the residue and should be discarded.

Crossword Puzzle

Across
1. hydrogen ______ is a color gas with a smell of rotten eggs
5. The major components in solution
6. Melting point and boiling point are _______ properties
7. Two elements are liquid at room temperature are mercury and _______
Down
2. In colloids ,The particles are called the ______ phase and the medium in which they are distributed is called the dispersion medium.
3. amount of solute present per unit volume or mass of the solution or solvent
4. denser particles are forced to the bottom and the lighter particles stay at the top when spun rapidly

Ans: 
1. sulphide
2. dispersed
3. concentration
4.centrifugation
5. solvent
6. physical
7. bromin

Multiple Choice Questions

Q.1. Kerosene and Petrol are miscible liquids. The difference between their boiling points is more than 25°C. The two liquids can be separated from each other by _____. 

(a) Simple distillation

(b) Steam distillation

(c) Fractional distillation

(d) Any of these

Q.2. How can a saturated solution be made unsaturated?
(a) By heating the solution
(b) By cooling the solution
(c) By increasing the amount of solute
(d) By centrifugation of the solution

Q.3. The cause of Brownian movement is:
(a) Heat changes in liquid state
(b) Convection currents
(c) Impact of molecules of dispersion medium on on dispersed phase
(d) Attractive forces between the particles of dispersed phase and dispersion medium.

Q.4. In which of the following, dispersed phase is a liquid and dispersion medium is a gas? 
(a) Cloud
(b) Smoke
(c) Gel
(d) Soap bubble

Q.5. At room temperature, a non-metal which is a liquid is: 
(a) Sulphur
(a) Bromine
(a) Chlorine
(a) Nitrogen

Fill in the Blanks

1. Common salt is _________.

2. A mixture contains more than ______ substance mixed in ______ proportion.
3. Properties of a __________ are different from its constituent elements, whereas a _______ shows the properties of its constituting elements.
4. A solution is defined as a mixture that is_________
5. We can remove salts from a solution by using the process of _________
6. A pure substance has a fixed__________ or ______ at constant temperature.
7. An element is made up of only one kind of _________.
8. Miscible liquids are separated by ________ .
9. Immiscible liquids are separated by using a _______.
10. Filtered tea is a _________ mixture.
11. Alloy is a _______.
12. Sublimation of camphor is a _________ change.
13. Most common chemical change we observe in our routine life is rusting of______.

Very Short Answer Question 

Q.1. Classify the substances given in below figure into elements and compounds

Q.2. Give one example each of homogeneous and heterogeneous mixture.
Q.3. Name the apparatus by which mixture of oil and water can be separated.
Q.4. Is brass a mixture or a compound?
Q.5. What type of solution is an alloy? Liquid solution or solid solution
Q.6. A mixture consisting of two miscible liquids ‘A’ and ‘B’ whose boiling points differ by 50 C can be separated by which process?
Q.7. Give one example of solid- liquid homogeneous mixture.
Q.8. What is a Aqua regia?
Q.9. Which method is used to separate two immiscible liquids?
Q.10. Name two elements which are in liquid state at room temperature? 

Short Answer Types Questions

Q.1. Try segregating the things around you as pure substances or mixtures. 

Q.2. What is meant by a substance? 

Q.3. What type of mixtures are separated by the technique of crystallisation? 

Q.4. What is tyndall effect? Which kinds of solution show it?

Q.5. What is centrifugation? Where it is used?

Q.6. What is crystallization? Where is it used? Why is this better than simple evaporation technique?

Q.7. What is a colloid? What are its various properties?

Q.8. Write a method to separate different gases from air.

Q.9. Explain the following giving examples. 
(a) saturated solution 
(b) pure substance 
(c) colloid 
(d) suspension

Q.10. Write the steps you would use for making tea. Use the words solution, solvent, solute, dissolve, soluble, insoluble, filtrate and residue.

Also read: Worksheet Solutions: Is Matter Around Us Pure

Crossword Puzzle

Across
1. hydrogen ______ is a color gas with a smell of rotten eggs
5. The major components in solution
6. Melting point and boiling point are _______ properties
7. Two elements are liquid at room temperature are mercury and _______
Down
2. In colloids ,The particles are called the ______ phase and the medium in which they are distributed is called the dispersion medium.
3. amount of solute present per unit volume or mass of the solution or solvent
4. denser particles are forced to the bottom and the lighter particles stay at the top when spun rapidly

Multiple Choice Questions

Q.1. According to ancient philosophers matter consists of: 
(a) Three constituents 
(b) Four constituents 
(c) Five constituents 
(d) Six constituents.

Correct Answer is Option (c)
Matter is made up of five constituents also called tatvas (air, water, earth, fire and sky).

Q.2. Dry ice is:
(a) Solid ammonia
(b) Solid carbon dioxide
(c) Solid sulphur dioxide
(d) Normal ice

Correct Answer is Option (b)
Dry ice is solid carbon dioxide (CO₂).

Q.3. Which of the following statements is not correct for liquid state?
(a) Particles are loosly packed in the liquid state
(b) Fluidity is the maximum in the liquid state
(c) Liquids can be compressed
(d) Liquids take up the shape of any container in which these are placed

Correct Answer is Option (b)
Fluidity is maximum in the gaseous state and not in the liquid state.

Q.4. Which of the following will sublime? 
(a) Common salt 
(b) Sugar 
(c) Camphor 
(d) Potassium nitrate

Correct Answer is Option (c)
Camphor, ammonium chloride, Phenophthelene sublimes i.e. change from solid to gaseous state directly without passing through liquid state upon heating.

Q.5. When the liquid starts boiling, the further heat energy which is supplied: 
(a) Is lost to the surrounding as such 
(b) Increases the temperature of the liquid 
(c) Increases the kinetic energy of the particles in the liquid 
(d) Is absorbed as latent heat of vaporisation by the liquid

Correct Answer is Option (d)
Heat is absorbed as latent heat of vapourisation. As long as liquid is not boiled, the heat energy which is supplied increases the kinetic energy of particles present in water. Once the liquid starts boiling the heat energy is used to brinchange in the state (liquid-gas). It is known as latent heat of vapourisation.

Fill in the Blanks

1. Matter is made up of small_________.

Correct Answer is Particles

2. The forces of attraction between the particles are _______ in solids, ______ in liquids and _________ in gases.

Correct Answer is Maximum, intermediate, minimum

3. __________ is the change of gaseous state directly to solid state without going through liquid state, and vice-versa.

Correct Answer is Deposition or Desublimation. 

4. Evaporation causes __________.

Correct Answer is Cooling

5. Latent heat of fusion is the amount of heat energy required to change 1 kg of solid into liquid at its ________.

Correct Answer is Melting point

6. Solid, liquid and gas are called the three _______ of matter.

Correct Answer is States

7. The smell of perfume gradually spreads across a room due to ______.

Correct Answer is Diffusion

8. Rapid evaporation depends on the ______ area exposed to atmosphere.

Correct Answer is Surface

9. As the temperature of a system increases, the pressure of the gases ______.

Correct Answer is Increases

10. As the volume of a specific amount of gas decreases, it’s pressure _______.

Correct Answer is Increases

11. As the temperature of a gas decreases, It’s volume ______.

Correct Answer is Decreases

12. Gas molecules at higher temperatures have more _______ than at cooler temperatures.

Correct Answer is Kinetic energy

13. A sponge has minute ________, in which ________ is trapped.

Correct Answer is holes, air.

14. The pressure inside of a sealed tube if you raise the temperature go ______

Correct Answer is Up

15. Forces of attraction in liquids are _______ than in solid.

Correct Answer is Weaker

16. Latent heat of ________ is the amount of heat energy required to change 1 kg of solid into liquid at its melting point.

Correct Answer is fusion

Very Short Answer Questions

Q.1. Name one property which is shown by naphthalene and not by sodium chloride.

Naphthalene undergoes sublimation upon heating i.e. it directly changes into vapours. Whereas Sodium chloride (common salt) does not undergo sublimation. It melts on strong heating.

Q.2. A rubber band changes its shape when stretched. Can it be regarded as solid?

Rubber is a solid. It has elastic property due to which it undergoes change in shape when pressure is applied and regains its original shape when pressure is released.

Q.3. Gases can be compressed but solids cannot. Explain.

In gases, interparticle spaces are quite large. On applying pressure, these spaces decrease and the molecules of gas come closer. As a result, the gases can be compressed. Whereas in solids, particles are compactly packed leaving negligible interparticle space thus solids cannot be compressed.

Q.4. Define latent heat of vaporization.

Latent heat of vaporization is the heat energy required to change 1 kg of a liquid to gas at atmospheric pressure at its boiling point.

Q.5. What happens to the heat energy which is supplied to the solid once it has started melting?

Once the solid has started melting heat energy absorbed is consumed in bringing about the change in state from solid to liquid (overcoming the force of attraction between the particles of solids). The heat absorbed is known as latent heat of fusion.

Q.6.The freezing point of water is 0°C. What is the corresponding temperature on the Kelvin scale?

Temperature on Kelvin scale = 0°C+273 = 273K.

Q.7. Are the melting point temperature of the solid state and the freezing point temperature of the liquid state of a substance different?

No, these are the same. For example, melting point of ice and freezing point of water are both 0°C or 273 K.

Q.8. A substance is in liquid state at room temperature and changes into gas upon heating. What will you call its gaseous state?

The gaseous state of the substance is called vapour. Gaseous state of a substance which exists as liquid also is known as vapour.

Q.9. When a crystal of copper sulphate is placed at the bottom of a beaker containing water, the colour of water slowly becomes blue, why?

Copper sulphate on dissolution in water releases (Cu²⁺ ions) and SO₄^2– ions. Due to diffusion of Cu²⁺ ions the colour of water slowly becomes blue.

Q.10. The boiling point of ethyl alcohol is 78°C. What is the corresponding temperature on kelvin scale?

Temperature on kelvin scale = 78 + 273 = 351 K

Crossword Puzzle

Across
1. BEC stands for Bose-Einstein-______
3. The state consists of super energetic and super excited particles
8. Conversion of solid to vapour is called ______
Down
2. This is the phenomenon of change of a liquid into vapours at any temperature below its boiling point
4. SI unit of Temperature
5. CNG stands ____ natural gas
6. It is the amount of water vapour present in air.
7. LPG stands for ______petroleum gas.

Answer: 

1. Condensation
2. evaporation
3. plasma
4. kelvin
5. Compressed
6. Humidity
7. liquefied
8. sublimation

Multiple Choice Questions

Q.1. According to ancient philosophers, matter consists of:
(a) Three constituents
(b) Four constituents
(c) Five constituents
(d) Six constituents

Q.2. Dry ice is:
(a) Solid ammonia
(b) Solid carbon dioxide
(c) Solid sulphur dioxide
(d) Normal ice. 

Q.3. Which of the following statements is not correct for liquid state?
(a) Particles are loosly packed in the liquid state
(b) Fluidity is the maximum in the liquid state
(c) Liquids can be compressed
(d) Liquids take up the shape of any container in which these are placed

Q.4. Which of the following will sublime? 
(a) Common salt
(b) Sugar
(c) Camphor
(d) Potassium nitrate

Q.5. When the liquid starts boiling, the further heat energy which is supplied: 
(a) Is lost to the surrounding as such
(b) Increases the temperature of the liquid
(c) Increases the kinetic energy of the particles in the liquid 
(d) Is absorbed as latent heat of vaporisation by the liquid

Fill in the blanks:-

1. Matter is made up of small_________.
2. The forces of attraction between the particles are _______ in solids, ______ in liquids and _________ in gases.
3. __________ is the change of gaseous state directly to solid state without going through liquid state, and vice versa.
4. Evaporation causes __________.
5. Latent heat of fusion is the amount of heat energy required to change 1 kg of solid into liquid at its ________.
6. Solid, liquid and gas are called the three _______ of matter.
7. The smell of perfume gradually spreads across a room due to ______.
8. Rapid evaporation depends on the ______ area exposed to the atmosphere.
9. As the temperature of a system increases, the pressure of the gases ______.
10. As the volume of a specific amount of gas decreases, it’s pressure _______.
11. As the temperature of a gas decreases, I’s volume ______.
12. Gas molecules at higher temperatures have more _______ than at cooler temperatures.
13. A sponge has minute ________, in which ________ is trapped.
14. The pressure inside of a sealed tube if you raise the temperature go ______
15. Forces of attraction in liquids are _______ than in solid.
16. Latent heat of ________ is the amount of heat energy required to change 1 kg of solid into liquid at its melting point.

Very Short Answer Questions

Q.1. Name one property which is shown by naphthalene and not by sodium chloride.

Q.2. A rubber band changes its shape when stretched. Can it be regarded as solid?

Q.3. Gases can be compressed but solids cannot. Explain.

Q.4. Kelvin scale of temperature is regarded better than the Celsius scale. Assign reason.

Q.5. What happens to the heat energy which is supplied to the solid once it has started melting?

Q.6. The freezing point of water is 0°C. What is the corresponding temperature on the Kelvin scale?

Q.7. Are the melting point temperature of the solid state and the freezing point temperature of the liquid state of a substance different?

Q.8. A substance is in liquid state at room temperature and changes into gas upon heating. What will you call its gaseous state?

Q.9. When a crystal of copper sulphate is placed at the bottom of a beaker containing water?

Q.10. The boiling point of ethyl alcohol is 78°C. What is the corresponding temperature on kelvin scale?

Crossword Puzzle

Across
1. BEC stands for Bose-Einstein-______

3. The state consists of super energetic and super excited particles

8. Conversion of solid to vapour is called ______
Down
2. This is the phenomenon of change of a liquid into vapours at any temperature below its boiling point
4. SI unit of Temperature
5. CNG stands ____ natural gas
6. It is the amount of water vapour present in air.
7. LPG stands for ______petroleum gas. 

Introduction

Improvement in Food Resources refers to the methods aimed at increasing the quantity and quality of food produced through agriculture and animal husbandry to meet the growing demand for food sustainably.

As living organisms, food is essential for our growth, health, and overall development. We obtain food primarily from plants and animals through agriculture and animal husbandry. With India’s growing population, the demand for food is rising, and it is crucial to find ways to increase food production efficiently.

Various Food Resources

This chapter focuses on:

• The need to improve crop and livestock production to meet food demand.
• Successes like the Green Revolution and the White Revolution boosted food and milk production.
• The importance of sustainable practices in agriculture and animal husbandry to protect natural resources.
• The connection between food security, increased production, and access to food.
• Scientific methods like mixed farming, intercropping, and integrated farming improve yields without harming the environment.

Improvement in Crop Yields

Food Crops and Their Nutritional Benefits

• Cereals such as wheat, rice, maize, millets, and sorghum provide us with carbohydrates for energy.
• Pulses like gram (chana), pea (matar), black gram (urad), green gram (moong), pigeon pea (arhar), and lentil (masoor) supply us with protein.
• Oilseeds, including soybean, groundnut, sesame, castor, mustard, linseed, and sunflower, offer essential fats.
• Vegetables, spices, and fruits deliver a variety of vitamins and minerals, along with small amounts of proteins, carbohydrates, and fats.
• Fodder crops like berseem, oats, or Sudan grass are grown for livestock feed.
• 
• Different Types of Crops in India

In India, the production of food grains has increased fourfold from 1952 to 2010, while the area of land available for cultivation has only risen by 25%.

Factors Affecting Crop Growth

• Different crops need specific climatic conditions, temperature, and sunlight duration (photoperiods) to grow and complete their life cycles.
• Plants gather energy through photosynthesis, which relies on sunlight.
• During the Kharif season (June to October), crops like paddy, soybean, pigeon pea, maize, cotton, green gram, and black gram flourish.
• In the Rabi season (November to April), crops such as wheat, gram, peas, mustard, and linseed do well.

Major Activities for Improvement:

• Crop Variety Improvement: Enhancing crop types to maximise yields, ensuring high production under diverse conditions.
• Crop Production Improvement: Implementing methods to increase overall crop output.
• Crop Protection Management: Taking measures to protect crops from damage and loss.

Crop Variety Improvement

Methods for Crop Variety Improvement

• Breeding for beneficial traits: Selecting varieties with qualities such as disease resistance and high yields.
• Hybridisation: Crossing genetically different plants, which can be intervarietal, interspecific, or intergeneric.
• Genetic modification: Introducing specific genes to achieve desired traits in crops.

Try yourself:Which type of crops are grown for livestock feed?

• A.Cereals
• B.Pulses
• C.Oil seeds
• D.Fodder crops

The factors for which variety improvement is done are:

• Higher yield: To boost crop productivity per acre.
• Improved quality: Quality requirements vary by crop; for instance, baking quality is crucial in wheat, while protein quality is essential in pulses.
• Biotic and abiotic resistance: Creating varieties that can withstand diseases, insects, drought, salinity, and extreme temperatures.
• Change in maturity duration: Shorter periods from sowing to harvesting enhance economic viability, enabling multiple crops per year.
• Wider adaptability: Developing varieties that can thrive in various environmental conditions stabilises crop production.
• Desirable agronomic characteristics: Traits like height and branching are advantageous for fodder crops, while shorter plants are preferred in cereals to minimise nutrient consumption.

Crop Production Management

• In India, as in many other agriculture-focused countries, farming varies from small to very large farms.
• Consequently, farmers have differing amounts of land, resources, and access to information and technology.
• Financial conditions significantly influence the farming practices and technologies that farmers can adopt.
• Cultivation methods and crop yield depend on factors like weather, soil quality, and water availability.
• Since weather conditions, such as drought or floods, can be unpredictable, varieties that grow well in various climatic situations are beneficial.
• Similarly, varieties that tolerate high soil salinity have also been developed.

Nutrient Management

Plant Nutrients

• Essential nutrients: Plants need nutrients from air, water, and soil for growth. Air provides carbon and oxygen, water supplies hydrogen, and soil provides the other thirteen nutrients.
• Macro-nutrients: These are nutrients required in large amounts, including carbon, oxygen, hydrogen, and others from the soil.
• Micro-nutrients: These are needed in smaller quantities and are also supplied by the soil.

A lack of these nutrients can negatively impact plant growth, reproduction, and disease resistance.

Deficiency of these nutrients affects reproduction, growth, and susceptibility to diseases in plants.

Manure

Manure is an organic substance made from the decomposition of animal waste and plant materials. It is rich in organic matter and essential nutrients, which help improve soil fertility and support healthy plant growth.

Benefits of Manure:

• Enriches the soil by adding organic matter and nutrients.
• Improves soil structure, which:
  1. Increases water retention in sandy soils.
  2. Enhances drainage and reduces waterlogging in clayey soils.
• Environmentally friendly: It recycles biological and farm waste, reducing the dependence on chemical fertilisers and helping lower water pollution.

Manure

Types of Manure

       (i) Compost and vermicompost:

• Composting: This involves breaking down waste like animal dung and vegetable scraps to create nutrient-rich compost.
• Vermicomposting: In this method, earthworms are used to speed up decomposition, resulting in vermicompost.Vermicomposting

(ii) Green manure: Plants such as sun hemp or guar are grown before planting other crops. When these plants are turned into the soil, they enrich it with nitrogen and phosphorus.

Let’s Revise

Q: How does manure improve soil fertility?

Ans: Manure enriches the soil with organic matter and essential nutrients, improving its fertility.

Q: Why is green manure used before sowing crops?

Ans: Green manure adds nitrogen and phosphorus to the soil, enhancing nutrient availability for the next crop.

Fertilisers

• Fertilisers are commercially manufactured nutrients that provide nitrogen, phosphorus, and potassium.
• They are essential for promoting the healthy growth of leaves, branches, and flowers, leading to robust plants.
• Fertilisers play a major role in increasing crop yields, especially in intensive farming.
• Careful application of fertilisers is crucial, including the right amounts, timing, and following guidelines before and after use for full effectiveness.
• Excessive watering can wash fertilisers away, leading to water pollution.
• Repeated use of fertilisers in one area can harm soil fertility since the soil’s organic matter isn’t restored.
• Green manure, made by growing specific plants and turning them into the soil, enriches the soil with nitrogen and phosphorus.Fertilisers

Benefits and Considerations of Fertilisers

• Boosts plant growth: Fertilisers deliver key nutrients like nitrogen, phosphorus, and potassium, fostering healthy growth.
• Increases yields: When used correctly, fertilisers can enhance crop productivity in high-cost farming.
• Soil health impact: Regular use of fertilisers can deplete soil fertility as it does not replenish organic matter and can harm beneficial soil microorganisms.

Proper Application and Precautions

• While aiming for maximum crop yields, consider the quick benefits of fertilisers alongside the long-term advantages of manure for soil health.
• Fertilisers need to be applied carefully, focusing on the right amount and timing to ensure they are fully used by plants.

Organic farming is a method that minimises or eliminates the use of chemical fertilisers, herbicides, and pesticides. It maximises the use of organic manures, recycled farm waste such as straw and livestock dung, and employs natural agents like blue-green algae for creating biofertilisers. Additionally, neem leaves or turmeric can be used as natural pesticides during grain storage, promoting healthier farming systems.

Try yourself:

What are the factors that influence crop growth?

• A.Climate, temperature, and photoperiods
• B.Soil quality, water availability, and weather conditions
• C.Seed selection, crop nurturing, and crop protection
• D.Fertilizer response, disease resistance, and product quality

Organic Farming

• Organic farming reduces or eliminates the use of chemicals like fertilisers, herbicides, and pesticides.
• Instead, it focuses on maximising the use of organic manures, recycled farm waste (like straw and livestock excreta), and bio-agents, such as cultures of blue-green algae for biofertilisers.
• Additionally, neem leaves or turmeric can serve as bio-pesticides for grain storage.
• Healthy cropping systems, including mixed cropping, inter-cropping, and crop rotation, are used to enhance control of insects, pests, and weeds while providing essential nutrients to crops.

Try yourself:

What is the purpose of using fertilizers in farming?

• A.To speed up the decomposition process
• B.To produce nutrient-rich compost
• C.To promote plant growth and increase crop productivity
• D.To enrich the soil with nitrogen and phosphorus

Also read: NCERT Solutions – Improvement in Food Resources

Irrigation

Proper irrigation is very important for the success of crops. Most agriculture in India relies on rain, meaning the success of crops in many areas depends on timely monsoons and adequate rainfall throughout the growing season. Therefore, poor monsoons can lead to crop failure. Ensuring that crops receive water at the right times during their growing season can boost the expected yields of any crop.

Irrigation

Types of Irrigation Systems

• Wells: There are two types of wells: dug wells and tube wells. A dug well collects water from shallow water-bearing layers, while a tube well can reach deeper water sources. Pumps are used to lift water from these wells for irrigation.
• Canals: This is usually a large and complex irrigation system. Canals receive water from one or more reservoirs or rivers. The main canal splits into branch canals, which have further distributaries to irrigate fields.
• River lift system: In areas where canal flow is inconsistent due to insufficient reservoir release, this system is more effective. Water is taken directly from rivers to support irrigation in nearby areas.
• Tanks: These are small storage reservoirs that collect and store runoff from smaller catchment areas. New initiatives to increase available water for agriculture include rainwater harvesting and watershed management. This involves creating small check dams, which help raise groundwater levels. The check dams prevent rainwater from flowing away and reduce soil erosion.

Droughts occur due to a lack or irregular distribution of rain. Drought poses a risk to rain-fed farming areas, where farmers rely solely on rain for crop production. Light soils hold less water, and in such areas, crops are negatively affected by drought conditions.

Try yourself:In which irrigation system is water directly drawn from rivers?

• A.Wells
• B.Canals
• C.River lift system
• D.Tanks

Cropping Patterns

Cropping patterns refer to various methods of growing crops to achieve the best results. 

Types of Cropping Patterns

• Mixed cropping: Growing two or more crops at the same time on the same land, such as wheat with gram, wheat with mustard, or groundnut with sunflower. This method reduces the risk of disease and helps protect against crop failure.
• Inter-cropping: Planting two or more crops together in a specific pattern, like rows of soybean alternating with rows of maize, or finger millet (bajra) with cowpea (lobia). This ensures that each crop has different nutrient needs, optimising nutrient use and reducing pest and disease spread.
• Crop rotation: Growing different crops on the same land in a planned sequence. The choice of crops depends on moisture availability and irrigation. Proper crop rotation can allow for two or three successful harvests in a year.

Crop Protection Management

• Field crops face many threats from weeds, insects, and diseases. Managing these threats timely manner is crucial to avoid significant crop damage and losses.
• Weeds: Unwanted plants in the fields, such as Xanthium (gokhroo), Parthenium (gazar ghas), and Cyperus rotundus (motha). They compete for resources, reducing crop growth. Therefore, removing weeds early is essential for a good harvest.
• Insect pests: They harm plants in three main ways: by cutting roots, stems, and leaves; by sucking sap; and by boring into stems and fruits, all of which can lower crop health and yields.
• Diseases: Caused by pathogens like bacteria, fungi, and viruses, which can spread through the soil, water, and air, leading to reduced crop health.

Let’s Revise

Q: What is inter-cropping?  Name a crop combination used in intercropping.

Ans: Inter-cropping involves growing two or more crops in a definite pattern, such as alternating rows. Soybean and maize is a common inter-cropping pair.

Q: How do insect pests damage crops?

Ans: By cutting parts, sucking sap, or boring into stems and fruits.

Methods of Control

• Pesticides: These include herbicides, insecticides, and fungicides, which are applied to crops or seeds and soil. However, overuse can be harmful to various plants and animals, and it can lead to pollution of the environment.
• Mechanical removal: This involves physical methods, such as manual weeding, to manage weed growth.
• Preventive measures:
  • Seed bed preparation: Properly preparing the seed bed and timely sowing of crops can help prevent weed growth.
  • Intercropping & crop rotation: Planting multiple crops together or rotating them can lessen the impact of pests and diseases.
  • Resistant varieties: Using crop varieties that resist pests and diseases.
  • Summer ploughing: Deep ploughing in summer to eliminate weeds and pests, reducing their effect on future crops.

Try yourself:

What is the main objective of organic farming?

• A.To maximize the use of chemicals in farming practices.
• B.To minimize the use of chemicals and maximize the use of organic manures and bio-agents.
• C.To promote the use of chemical fertilizers and pesticides for higher crop yields.
• D.To rely solely on chemical fertilizers and pesticides for crop protection.

Storage of Grains

Storage losses in agricultural products can be quite high. The causes of these losses are biotic factors—like insects, rodents, fungi, mites, and bacteria—and abiotic factors, such as improper moisture and temperature in storage. These issues can lead to:

• Decline in quality
• Weight loss
• Reduced germination
• Discolouration of produce
• Poor marketability

Control Measures

Preventive Measures

• Preventive and control measures are implemented prior to storing grains.
• Thorough cleaning of the produce is essential.
• Proper drying should be done in both sunlight and shade.
• Fumigation with pest-control chemicals is necessary.
• Effective seedbed preparation, timely sowing of crops, intercropping, and crop rotation assist in controlling weeds.
• Utilising resistant varieties and summer ploughing can help eliminate weeds and pests.

Systematic Warehouse Management

• This is vital for minimising storage losses.
• The process involves organised treatment of grains and effective management of warehouses.

Animal Husbandry

• Animal husbandry is the scientific management of livestock, which includes activities such as feeding, breeding, and controlling diseases.
• This type of farming involves animals like cattle, goats, sheep, poultry, and fish.
• As the population grows and living standards improve, the demand for milk, eggs, and meat also increases.
• Moreover, there is a heightened awareness about the humane treatment of livestock, leading to new considerations in farming practices.
• Therefore, there is a need to enhance livestock production to meet these rising demands.

Cattle Farming

• Cattle farming serves two main purposes: producing milk and providing draught power for agricultural tasks like ploughing, watering, and transporting goods.
• In India, cattle are classified into two species: Bos indicus (cows) and Bos bubalis (buffaloes).
• Female animals that produce milk are referred to as milch animals, while those used for labour are known as draught animals.
• The amount of milk produced is influenced by the lactation period, which is the time after a calf is born during which the mother produces milk.
• This production can be enhanced by extending the lactation period.
• Exotic breeds (like Jersey and Brown Swiss) are often chosen for their longer lactation periods, whereas local breeds (such as Red Sindhi and Sahiwal) are known for their strong disease resistance.
• Cross-breeding these types can result in animals that possess both desirable traits.
• Animals like cows and buffalo need clean shelters for their health and to ensure they produce clean milk. They should be kept in well-ventilated sheds that protect them from rain, heat, and cold. The floor of the shed should slope to stay dry and make cleaning easier.
  Cattle Farming

Feeding Requirements

• Dairy animals have two types of nutritional needs: 
  (a) maintenance requirement, which keeps them healthy, and 
  (b) milk-producing requirement, which is essential during lactation. 
• Animal feed consists of
  (a) roughage, which is high in fibre, and
  (b) concentrates, which are lower in fibre but rich in proteins and nutrients. 

Cattle require a balanced diet that provides all necessary nutrients in the right proportions. Certain feed additives containing micronutrients can also enhance the health and milk yield of dairy animals.

Diseases and Control

• Cattle suffer from various diseases that reduce milk production and may cause death. 
• Healthy cattle eat regularly and have normal posture. 
• Parasites can be external (causing skin diseases) or internal, like worms affecting the stomach and flukes damaging the liver. 
• Bacterial and viral infections also occur, for which vaccinations are given.

Let’s Revise

Q: What are milch animals?

Ans: Milch animals are female animals that produce milk.

Q: Name one exotic and one local breed of cattle.

Ans: Exotic: Jersey; Local: Sahiwal.

Poultry Farming

Poultry farming is the practice of raising birds like chickens for their eggs and meat. Special poultry breeds are created for specific roles: layers produce eggs, while broilers are bred for meat. Cross-breeding between local Indian breeds, such as the Aseel, and foreign breeds like the Leghorn aims to create new varieties with desirable characteristics, which include:

• High numbers and quality of chicks;
• Dwarf broiler parents for commercial chick production;
• Ability to adapt to hot weather;
• Low maintenance needs;
• Smaller egg-laying birds can thrive on cheaper, more fibrous diets made from agricultural by-products.

Egg and Broiler Production

Broiler chickens are raised specifically for meat and sent to market when they are ready. Their diet is rich in protein and contains sufficient fat. The poultry feed includes high levels of vitamins A and K to promote optimal growth and efficient feed usage. Care is taken to minimise mortality and maintain the quality of feathers and meat.

Importance of Good Management Practices

Good management practices are crucial for successful poultry production. This includes:

• Maintaining the housing at the correct temperature;
• Ensuring the environment and feed are clean, which involves regular cleaning, sanitation, and disinfection;
• Preventing and managing diseases and pests through appropriate vaccination which can stop infectious diseases and reduce poultry losses during outbreaks.

The housing, nutritional, and environmental needs of broilers differ somewhat from those of egg layers.

Broilers have different housing, nutritional, and environmental needs compared to egg layers. Their specific diet is designed to support their growth requirements.

Disease Prevention and Control

Poultry can become ill due to:

• Viruses
• Bacteria
• Fungi
• Parasites
• Nutritional deficiencies

Regular cleaning, sanitation, and disinfectant spraying are essential.

• Vaccinations can help prevent infectious diseases and reduce poultry losses during outbreaks.
• Farm animals receive vaccinations against major viral and bacterial diseases.

Poultry in India is the most efficient at converting low-fibre food (not suitable for human consumption) into nutritious animal protein.

Try yourself:

What are the two main purposes for which improved poultry breeds are developed?

• A.Egg production and meat production
• B.Egg production and dairy production
• C.Egg production and wool production
• D.Meat production and wool production

Fish Production

• The main aim is that fish serves as an affordable source of protein in our meals.
• Fish production includes various species, such as true finned fish and shellfish like prawns and molluscs.
• Fish can be obtained in two ways: through natural resources, known as capture fishing, or through farming, referred to as culture fishery.
• Fish are found in both seawater and freshwater environments. Marine fisheries and inland fisheries are two major sources.

Marine Fisheries

• India’s marine fishery resources include 7500 km of coastline and the deep seas beyond it.
• Popular marine fish found in these waters include pomfret, mackerel, tuna, sardines, and Bombay duck.
• Marine fish are caught using various fishing nets from fishing boats.
• Yields are increased by locating large schools of fish in the open sea using satellites and echo-sounders.
• Some marine fish of high economic value are also farmed in seawater, including finned fish like mullets, bhetki, and pearl spots, shellfish such as prawns, mussels, and oysters, as well as seaweed.
• In such a system, a combination of five or six fish species is used in a single fishpond to avoid competition for food.

Aquaculture in Seawater

• Certain valuable marine fish are grown in seawater through a method called mariculture.
• Examples of farmed finned fish include mullets, bhetki, and pearl spots. Shellfish like prawns, mussels, and oysters are also cultivated.
• Seaweed is another product obtained from mariculture, and oysters are cultivated not only for their meat but also for pearl production.
• As stocks of marine fish are depleted, the demand can only be met through cultured fisheries, a practice known as mariculture.

Let’s Revise: Besides meat, why are oysters cultivated?

Ans: For pearl production.

Inland Fisheries

Inland Fisheries

• Freshwater resources consist of canals, ponds, reservoirs, and rivers.
• Brackish water areas, like estuaries and lagoons, are also important for fish.
• While fish are captured in these inland waters, most production comes from aquaculture.

Aquaculture in Freshwater Systems

• Freshwater aquaculture involves raising fish in resources like canals, ponds, reservoirs, and rivers. Fish can also be cultivated in paddy fields, where they grow alongside rice crops, making efficient use of water and land.
• An intensive method used in freshwater aquaculture is composite fish culture, where both local and imported species are reared together. In this system, fish species are carefully selected to avoid competition for food by occupying different zones of the pond:
  – Catlas feed at the surface,
  – Rohus feed in the middle layer,
  – Mrigals and Common Carps feed at the bottom,
  – Grass Carps consume aquatic weeds.
• This arrangement ensures that all available food in the pond is utilised efficiently, resulting in a higher overall fish yield.
• However, a major challenge in this system is that many fish species breed only during the monsoon. Additionally, fish seed collected from natural sources may get mixed with other species, affecting the purity and quality of the stock.
• To address this issue, scientists have developed methods to breed fish in ponds using hormonal stimulation, which ensures the year-round availability of pure and healthy fish seed in the desired quantities.

Challenges in Fish Farming

• Many fish types in composite fish culture only breed during the monsoon season.
• A significant issue in fish farming is the shortage of quality fish seed.
• To solve this problem, methods have been developed to breed these fish in ponds using hormonal stimulation, ensuring a reliable supply of pure fish seed in the required amounts.

Bee-Keeping

Bee-keeping for honey production is a farming activity. Besides honey, beehives also provide wax, which is used in many medicinal products.

• Local bee varieties, such as Apis cerana indica (the Indian bee), A. dorsata (the rock bee), and A. florae (the little bee), are used alongside the Italian bee (A. mellifera) for commercial honey production.
• The Italian bees have high honey collection capacity, sting somewhat less, and stay in a given beehive for long periods.
• The quality of honey depends on the pasturage, and bee farms or apiaries are established for commercial honey production.
• Honey production also provides wax, which is used in various medicinal preparations.

Factors Affecting Honey Quality

• The quality of honey relies on the availability of flowers that bees can gather nectar and pollen from.
• Besides having enough flowers, the types of blooms influence the flavour of the honey.
• Italian bees are known for their high honey production. They are less aggressive, remain in the same hive for extended periods, and breed effectively

Understanding Sound

Sound is an essential part of our everyday life, coming to us in many different forms. But what is sound exactly?

Sound is a type of energy that creates a sensation of hearing. It is made by vibrations and travels in waves. It is important to understand that sound waves are a kind of mechanical wave, which means they need a medium (like air, water, or solids) to move through.

Key Characteristics of Sound

• Nature of Sound: Sound is produced by vibrations and travels in waves.
• Transmission: Sound requires a medium (such as air, water, or solids) to travel.
• Loudness and Intensity: Loudness is how our ears respond to the intensity of sound.
• Audible Range: The typical range of hearing for most people is between 20 Hz and 20 kHz. Sounds below this range are called ‘infrasonic’, while those above are called ‘ultrasonic’.

When you clap, you create a sound. But can you make sound without using any energy? In this chapter, we will explore how sound is made, how it travels through different mediums, and how it is detected by our ears.

Production of Sound

Sound is created by objects that vibrate. It is a type of energy that we hear with our ears. When objects vibrate, they generate sound waves made of compressions and rarefactions, which are key to understanding how sound moves through the air. A compression is a part of the sound wave where the pressure is higher, while rarefaction is where the pressure is lower.

Activity:

Vibrating tuning fork just touching the suspended Table Tennis ball

• Objective: Observe how vibrations create sound and influence nearby objects.
• Materials: Tuning fork, rubber pad, small ball (table tennis or plastic), thread, needle.
• Procedure:
  1. Strike the tuning fork against the rubber pad to make it vibrate.
  2. Hold the vibrating fork near your ear and listen to the sound.
  3. Touch a vibrating prong with your finger and feel the vibrations.
  4. Hang a small ball using a thread. Lightly touch the ball with the vibrating fork and watch how it moves.
• Observations:
  1. The vibrating fork makes sound.
  2. Touching the prong lets you feel the vibrations.
  3. The ball moves when it is touched by the vibrating fork.
• Conclusion: Vibrations create sound, and sound can also be produced by plucking, scratching, rubbing, blowing, or shaking different objects.

Sound can be generated through various actions that cause objects to vibrate. Vibration means the quick back-and-forth movement of an object. The sound of a human voice comes from vibrations in the vocal cords. When a stretched rubber band is plucked, it vibrates and makes sound.

• Compression is the area of high pressure in a sound wave.
• Rarefaction is the area of low pressure in a sound wave.

In brief, sound is made by vibrating objects, and grasping the ideas of compression and rarefaction is important for understanding how sound travels through different materials.

Try yourself:What is vibration?

• A.The production of sound through striking objects
• B.The motion of an object from side to side
• C.The rapid to and fro motion of an object
• D.The buzzing sound produced by bees

Propagation of Sound

Sound Propagation and Waves:

• A wave is a disturbance that travels through a medium, causing its particles to move and set nearby particles in motion.
• The particles themselves do not move forward; rather, the disturbance moves forward.
• Sound can be thought of as a wave because it is the movement of particles in a medium.
• Sound waves are known as mechanical waves because they depend on the movement of particles.
• Sound can be seen as variations in density or pressure in the medium.

Sound Propagation in Air:

• Air is the most common medium for sound transmission.
• When a vibrating object moves forward, it compresses the air in front of it, creating a high-pressure area known as compression (C).
• This compression then moves away from the vibrating object.
• When the object moves backward, it creates a low-pressure area called rarefaction (R).
• As the object oscillates quickly, it produces a series of compressions and rarefactions in the air, forming the sound wave.
• Compression indicates high pressure, whereas rarefaction indicates low pressure.

 Compression (C) & Rarefaction (R) of sound 

• Pressure relates to the number of particles in a given volume of the medium.
• A higher density of particles results in more pressure, and a lower density results in less pressure.
• The distance between two consecutive compressions or rarefactions is known as the wavelength, λ.
• The time taken for one complete oscillation of the density or pressure is called the time period, T.
• The speed (v), frequency (f), and wavelength (λ) of sound are connected by the equation: v = fλ.

The law of reflection of sound states that the angles of incidence and reflection are equal concerning the normal to the reflecting surface at the point of incidence, and all three lie in the same plane.

Sound Waves are Longitudinal Waves

• A wave is a disturbance that travels through a medium, causing its particles to move and set nearby particles in motion. The individual particles do not move forward themselves; instead, the disturbance moves through the medium.
• Sound travels through the medium by a series of compressions (C) and rarefactions (R). These areas of closely packed and spaced out particles create longitudinal waves.
• In longitudinal waves, the particles of the medium move in the same direction as the wave is travelling. They oscillate back and forth around their resting position without changing their location.
• Sound waves are defined by how the particles in the medium move and are classified as mechanical waves. Air is the most common medium for sound transmission.

How Sound Waves Work

• When a vibrating object moves forward, it compresses the air in front, creating a high-pressure area known as a compression (C).
• When the object moves backward, it creates a low-pressure area called a rarefaction (R). Compression refers to high pressure, while rarefaction refers to low pressure.
• Pressure is linked to the number of particles in a given volume; a denser medium results in higher pressure, and a less dense medium results in lower pressure.

Transverse Waves

• Another type of wave is called a transverse wave. In these waves, particles do not move in the same direction as the wave travels but rather move up and down around their average position.
• This means that in transverse waves, the individual particles move at a right angle to the direction of wave travel.
• An example of a transverse wave is the ripples created on the surface of water when a pebble is dropped into it.

Try yourself:In longitudinal waves, how do particles of the medium move in relation to the direction of wave propagation?

• A.Perpendicular to the direction of wave propagation
• B.Parallel to the direction of wave propagation
• C.Back and forth around their position of rest
• D.They remain stationary

Characteristics of a Sound Wave

We can describe a sound wave by its:

• Frequency
• Amplitude
• Speed

Key Characteristics of Sound Waves

• Sound waves can be described by their frequency, amplitude, and speed.
• The density and pressure of the medium change with distance as the sound wave travels.
• Compressions are areas of high density and pressure, while rarefactions are areas of low pressure.
• Wavelength is the distance between two consecutive compressions or rarefactions, represented by λ (lambda) with the SI unit of metre.
• Frequency represents the number of oscillations per unit time and is measured in hertz (Hz), usually represented by ν (Greek letter, nu).
• The time period (T) is the time taken for one complete oscillation, and frequency and time period are inversely related.
• The audible range of hearing for average human beings is in the frequency range of 20 Hz – 20 kHz.
• Sound waves with frequencies below the audible range are called “infrasonic,” and those above are called “ultrasonic.”

Pitch, Amplitude, and Loudness

• Pitch is determined by the frequency of the sound wave, where higher frequency corresponds to a higher pitch.
• Amplitude refers to the size of the maximum disturbance in the medium.
• Loudness is a response of the ear to the intensity of sound, with greater amplitude producing a louder sound.
• The loudness of a sound decreases as it travels further from its source.

Quality and Speed of Sound

• Quality or timbre refers to the feature that distinguishes one sound from another with the same pitch and loudness.
• Sound waves with a single frequency are called tones, while those with a mix of frequencies are called notes.
• The speed of sound is the distance travelled by a point on a wave per unit time, calculated as Speed of sound = wavelength × frequency.

• The speed of sound depends mainly on the nature and the temperature of the transmitting medium.

Intensity of Sound

• Intensity of sound refers to the amount of sound energy passing through a unit area per second.
• Loudness is a response of the ear to the intensity of sound.
• Even sounds with the same intensity can be heard as different loudness due to differences in the ear’s sensitivity.

Speed of Sound In Different Media

• Sound travels through a medium at a finite speed, which is slower than the speed of light.
• The speed of sound depends on the properties of the medium and is affected by temperature; as temperature rises, the speed of sound in the medium increases.
• The speed of sound varies in different media at a given temperature and decreases when moving from a solid to a gas.
• Raising the temperature in a medium generally increases the speed of sound.

What is the definition of sound?

• A.Sound is a type of energy that makes us see things through our eyes.
• B.Sound is a form of energy that makes us hear things through our ears.
• C.Sound is a type of energy that makes us taste things with our tongues.
• D.Sound is a form of energy that makes us feel things with our hands.

Reflection of Sound

• • Sound waves behave like a rubber ball bouncing off a wall when they hit a solid or liquid surface.
  • Similar to light, sound follows the laws of reflection that you may have studied before.
  • When sound strikes a surface, it reflects in such a way that the angles of incidence and reflection are equal in relation to the normal (a line that is perpendicular to the surface) at the point where it hits.
  • These angles and the normal line are all in the same plane.
  • For sound waves to reflect, they need a sufficiently large obstacle, regardless of whether it is smooth or rough.

Echo

• An echo is the sound we hear when the original sound is bounced back to us. The sensation of sound lingers in our brain for about 0.1 seconds.
• Yelling or clapping near a suitable reflecting surface can create an echo.

Man producing echo

Conditions for Hearing a Distinct Echo

• To hear a clear echo, there must be a time gap of at least 0.1 seconds between the original sound and the reflected sound. If we consider the speed of sound to be 344 m/s at a temperature of 22 °C in air, the total distance the sound travels must be at least (344 m/s) × 0.1 s = 34.4 m.
• For a distinct echo, the minimum distance between the sound source and the reflecting surface should be half of the total distance, which is 17.2 metres. This distance can change depending on the temperature of the air.

Echoes can happen more than once because of repeated reflections.

Reverberation

When a sound is made in a large hall, it continues to exist because of multiple reflections from the walls until its intensity decreases enough that it can no longer be heard. This ongoing presence of sound due to reflections is known as reverberation.

Reverberation of Sound

• • Too much reverberation in an auditorium or large hall is not desirable.
  • To reduce reverberation, the walls and ceiling of the auditorium are usually covered with materials that absorb sound, such as compressed fibreboard, rough plaster, or curtains.
  • Additionally, the materials used for seating are selected for their sound-absorbing properties.

Question: A person clapped his hands near a cliff and heard the echo after 2 s. What is the distance of the cliff from the person if the speed of sound, v, is taken as 346 m/s?

Solution: Given,

Speed of sound: 346 m/s

Time taken for hearing the echo: 2 s

Distance travelled by the sound

Distance = 346 m/s × 2 s = 692 m

In 2 seconds, sound travels twice the distance between the cliff and the person.

Therefore, the distance between the cliff and the person is: Distance = 692 m / 2 = 346 m

Minimum Distance for Distinct Echoes

• To hear distinct echoes, the minimum distance of the obstacle from the source of sound must be half of the total distance covered by the sound, which is at least 17.2 m.
• This distance can change with temperature, as the speed of sound varies with temperature.

Uses of Multiple Reflections of Sound

• Megaphones and Loudhailers: These devices are made to direct sound in a specific direction rather than spreading it everywhere. They usually have a tube and a conical opening that reflect sound waves, directing most of the sound towards the audience.
• Stethoscopes: A stethoscope is a medical instrument used by doctors to listen to sounds inside the body, especially in the heart or lungs. The sound of the patient’s heartbeat reaches the doctor’s ears through multiple reflections of sound within the stethoscope.
• Auditoriums and Concert Halls: In concert halls, conference rooms, and cinemas, the ceilings are often curved to make sure that sound reaches every corner of the hall. This helps to spread sound evenly throughout the space. The rolling of thunder is another example, caused by the repeated reflections of sound from different surfaces, like clouds and the ground.

Curved ceiling of conference hall

Try yourself:What is the minimum time interval required for a distinct echo to be heard?

• A.0.01 seconds
• B.0.1 seconds
• C.1 second
• D.10 seconds

Range of Hearing

• The range of sound that humans can hear is from about 20 Hz to 20,000 Hz (where one Hz equals one cycle per second). Children under five years old and some animals, like dogs, can hear sounds up to 25 kHz (one kHz equals 1000 Hz).
• As people age, their ears become less responsive to higher frequencies.
• Sounds that are below 20 Hz are known as infrasonic sound or infrasound. If we were able to hear infrasound, we might perceive vibrations like those of a pendulum, similar to how we hear a bee’s wings.
• Rhinoceroses communicate using infrasound at frequencies as low as 5 Hz. Animals like whales and elephants also produce sounds in the infrasound range.
• It has been noted that some animals can detect low-frequency infrasound before earthquakes occur. Earthquakes generate low-frequency infrasound prior to the main shock waves, which may warn the animals.
• Frequencies above 20 kHz are referred to as ultrasonic sound or ultrasound. Animals such as dolphins, bats, and porpoises produce ultrasound.
• Certain moths have exceptionally sensitive hearing, enabling them to hear the high-frequency sounds made by bats, helping them to escape. Additionally, rats can create ultrasound during play.
• Ultrasound has various applications in both medical and industrial fields.

Try yourself:What is the upper limit of the audible range for children under five years old and some animals?

• A.10,000 Hz
• B.15,000 Hz
• C.20,000 Hz
• D.25,000 Hz

Applications of Ultrasound

1. Cleaning Hard-to-Reach Objects

• Objects are placed in a cleaning solution while ultrasonic waves are sent through it.
• The high frequency of the waves causes dust, grease, and dirt to detach and fall away.
• This method ensures thorough cleaning, even in complex shapes like spiral tubes or electronic components.

2. Detecting Cracks and Flaws

• Ultrasound is used to identify cracks and flaws in metal blocks used in construction.
• Ordinary sounds with longer wavelengths cannot detect these flaws as they bend around corners.
• Ultrasonic waves pass through the metal block, and detectors identify the transmitted waves.
• If there is a defect, the ultrasound reflects back, indicating the presence of a flaw.

3. Echocardiography

• Ultrasonic waves are reflected from different parts of the heart to create an image.
• Echocardiography is essential for diagnosing heart conditions and abnormalities.

4. Ultrasonography

• Ultrasonic waves are used to image internal organs of the human body.
• A doctor can examine organs like the liver, gall bladder, uterus, and kidneys.
• Changes in tissue density cause the waves to reflect, turning into electrical signals.
• These signals create images that help detect abnormalities, such as stones or tumours.
• Ultrasonography is especially useful during pregnancy to check for congenital defects and growth issues.

5. Medical Treatment: Kidney Stone Breakage

• Ultrasound can break small kidney stones into fine pieces.
• The fragments can then be flushed out through urine, avoiding invasive procedures.

Work, Power, and Energy

In earlier chapters, we learned about motion, its causes, and gravitation. Now, we explore another key idea—work, and its close partners, energy and power.

• Energy is what keeps both living beings and machines going. We use it for everything—from running, playing, and thinking to operating engines and machines. Animals, too, need energy to survive, move, and help in tasks like carrying loads or ploughing fields.
• Whether it comes from food or fuels like petrol and diesel, energy is what makes work possible. In this chapter, we’ll see how work and energy are connected and how they shape the world around us.

What is Work?

In our daily lives, we often refer to “work” as activities that require physical or mental effort. However, the scientific definition of work might differ from our usual understanding.

For instance, if you push a rock and it doesn’t move, even if you feel tired, scientifically, no work has been done. 

Scientific Conception of Work

In scientific terms, work is defined as applying force to an object that causes it to move. Work done is calculated by multiplying the force applied by the distance the object moves in the direction of that force. Here are a few examples to clarify this concept:

• Pushing a pebble: When you push a pebble and it moves, you apply force, and the pebble is displaced. Work is done here.
• Pulling a trolley: If a girl pulls a trolley and it moves, the force she applies and the trolley’s movement mean work is done.
• Lifting a book: When you lift a book, your force moves it upwards, so work is accomplished.

For work to occur, two key conditions must be satisfied:

• There must be an application of force on the object.
• The object must be displaced in the direction of the force.

It’s important to note that if there is no movement of the object, then the work done is zero. Additionally, an object capable of doing work is said to have energy.

Mathematically, the work done is calculated as: 

Work done = force x displacement

where:

• F is the constant force applied.
• S is the displacement in the direction of the force.

The SI unit of work is the joule (J or Nm). Work has magnitude but no direction.

In summary, work occurs when a force makes an object move in that direction, and it is measured by the product of force and distance moved.

Work is a fundamental concept linked to energy, which exists in different forms such as kinetic energy and potential energy. Understanding work is essential for learning about energy conservation and transformation.

Try yourself:What is the scientific definition of work?

• A.the product of force and displacement in the direction of the force
• B.Work is the physical or mental effort involved in an activity.
• C.Work is the conversion and transfer of energy in various systems.
• D.Work is the product of force and displacement, regardless of the direction.

Work Done By A Constant Force

Work done on an object is defined as the amount of force multiplied by the distance the object moves in the direction of the applied force. 

• Work has only magnitude and no direction. 
• The unit of work is joule: 
  1 Joule (J) = 1 Newton × 1 metre (N·m)
• Here, the unit of work is Newton metre (Nm) or joule (J). 
• Thus, 1 J is the amount of work done on an object when a force of 1 N displaces it by 1 m along the direction of the force.

Work done on an object by a force would be zero if the displacement of the object is zero.

Example 1

A force of 10 Newtons is applied to an object, causing it to be displaced by 5 meters. What is the work done on the object?

We can use the formula: W = F x S
Force (F) = 10 Newtons
Displacement (S) = 5 meters
Putting these values into the equation, we have:
W = (10 N) x (5 m) = 50 Joules

Therefore, the work done on the object is 50 Joules.

Example 2

A porter lifts a load of 15 kg from the ground and puts it on his head 1.5 m above the ground. Calculate the work done by him on the luggage.

• Mass of luggage, m = 15 kg
• Displacement, s = 1.5 m
• Work done, W = F × s = mg × s = 15 kg × 10 m/s² × 1.5 m = 225 kg m/s² m = 225 Nm = 225 J

Work done is 225 J.

Force at an Angle

When a force is applied at an angle to the direction of displacement, only a part of the force causes motion. The formula to calculate work in such cases is: Work = Force × Distance × cos(θ). 

Where:

• Force is the magnitude of the constant force applied.
• Distance is the displacement of the object in the direction of the force.
• θ is the angle between the force and the displacement.

If the force and displacement are in the same direction (θ = 0), the formula simplifies to: Work = Force × Distance. This means that work done by a constant force is equal to the product of the force applied and the distance over which the force acts.

Example 3

A box is pushed with a force of 50 N at an angle of 30° to the horizontal. If the box moves 10 m, calculate the work done.

• Force (F) = 50 N
• Angle (θ) = 30°
• Distance (d) = 10 m

Formula: Work = F × d × cos(θ)

Step-by-step solution:

Answer: The work done is approximately 433 J (Joules).

Positive, Negative & Zero Work Done

• Positive Work: Work is considered positive if the displacement of the object is along the direction of the force applied. 
  Example: Work done by a man is taken as positive when he moves from the ground floor to the second floor of his house.
• Negative Work: Work is taken as negative if the displacement of the object is in the direction opposite to the force applied. 
  Example: Work done by the man is negative when he descends from the second floor of the house to the ground floor.

Positive and Negative Work Done

• Zero Work Done: If the displacement of an object is in a direction perpendicular to the application of force, work done is zero despite the fact that force is acting and there is some displacement too. 
  Example: Imagine pushing a lawn roller forward. While gravity pulls it downward, the roller moves horizontally. Since gravity acts perpendicular to the roller’s movement, it does no work. This is an example of zero work, where a force doesn’t contribute to the displacement.

The gravitational potential energy of an object of mass m raised through a height, h, from the Earth’s surface is given by mgh.

Try yourself:The work done on an object does not depend upon the

• A.displacement
• B.force applied
• C.angle between force and displacement 
• D.initial velocity of the object 

What is Energy?

An object that can do work is said to have energy. Therefore, the energy of an object is its ability to perform work. When an object does work, it loses energy, while the object that receives the work gains energy. This means energy is transferred from one object to another. The unit of energy is the same as that of work, which is the joule (J). One joule is the energy needed to do one joule of work. A larger unit, the kilojoule (kJ), is also used, where 1 kJ equals 1000 J.

• An object with energy can apply force on another object.
• The energy of an object is measured by its ability to do work, indicating that any object with energy can perform work.

Energy Transformation

Forms of Energy

Energy exists in various forms in nature, including:

• Mechanical energy
• Heat energy
• Electrical energy
• Light energy
• Chemical energy
• Nuclear energy

Mechanical energy can be divided into two types:

• Kinetic energy
• Potential energy

Potential and Kinetic Energy

Kinetic Energy

The kinetic energy of an object is the energy possessed by it by virtue of its state of motion. A speeding vehicle, a rolling stone, a flying aircraft, flowing water, blowing wind, and a running athlete possess kinetic energy.

For an object of mass m and having a speed v, the kinetic energy is given by:

F = ma

Also, W=Fs

From the third equation of motion, we know that

v² – u² = 2as

Rearranging the equation, we get
s = v² – u²/2a

Substituting equation for work done by a moving body,

Taking initial velocity as zero, we get

where:

• E_k is the kinetic energy.
• m is the mass of the object.
• v is the velocity of the object

Note : When two identical bodies are in motion, the body with a higher velocity has more KE.

Potential Energy

An object gains energy when it is lifted to a higher position because work is done against the force of gravity. This energy is known as gravitational potential energy. Gravitational potential energy is defined as the work done to raise an object from the ground to a certain height against gravity.

Let’s consider an object with a mass m being lifted to a height h above the ground.

The minimum force required to lift the object is equal to its weight, which is mg(where g is the acceleration due to gravity).

The work done on the object to lift it against gravity is given by the formula:

Work Done (W) = Force × Displacement

W = mg × h = mgh

The energy gained by the object is equal to the work done on it, which is mgh units. 

This energy is the potential energy (E_p) of the object.

E_p = mgh

Note: It’s important to note that the work done by gravity depends only on the difference in vertical heights between the initial and final positions of the object, not on the path taken to move the object. For example, if a block is raised from position A to position B by taking two different paths, as long as the vertical height AB is the same (h), the work done on the object is still mgh.

Potential Energy of an Object at Height

Let’s consider an object with a mass m being lifted to a height h above the ground.

The minimum force required to lift the object is equal to its weight, which is mg (where g is the acceleration due to gravity).

The work done on the object to lift it against gravity is given by the formula:

Work Done (W) = Force × Displacement

W = mg × h = mgh

Since work done on the object is equal to mgh, an energy equal to mgh units is gained by the object. This is the potential energy (E_p) of the object.

Potential Energy (E_p) = mgh

Note: The work done by gravity depends only on the difference in vertical heights between the initial and final positions of the object, not on the path taken to move the object. For example, if a block is raised from position A to position B by taking two different paths, as long as the vertical height AB is the same (h), the work done on the object is still mgh.

Example 5

Find the energy possessed by an object of mass 10 kg when it is at a height of 6 m above the ground.
Given g = 9.8 m/s².

• Mass (m) = 10 kg
• Height (h) = 6 m
• Acceleration due to gravity (g) = 9.8 m/s²

Using the formula for potential energy: E_p = mgh

Substituting the values, we have:

Potential Energy = 10 × 9.8 × 6 = 588 J

Therefore, the potential energy of the object is 588 Joules.

Example 6

An object of mass 12 kg is at a certain height above the ground. If the potential energy of the object is 480 J, find the height at which the object is with respect to the ground. Given g = 10 m/s².

Mass of the object, m = 12 kg, potential energy, E = 480 J.

Using the formula E = mgh:

480 J = 12 × 10 × h

Solving for h:

h = 480 J / 120 kg m/s² = 4 m

The object is at a height of 4 m.

Also read: NCERT Solutions: Work and Energy

Law of Conservation of Energy

According to the law of conservation (transformation) of energy, we can neither create nor destroy energy. Energy can only change from one form to another; it cannot be created or destroyed. The total energy before and after the change remains constant. The total mechanical energy of an object is the sum of its kinetic energy and potential energy.

• For an object falling freely, the potential energy decreases as it falls and transforms into kinetic energy. This process does not break the law of conservation of energy; instead, it demonstrates it, since the total mechanical energy remains unchanged during the fall.
• As the object continues to fall, its potential energy decreases while its kinetic energy increases. If v is the object’s velocity at a given moment, the kinetic energy is 1/2 mv². Just before hitting the ground, h = 0, and v is at its maximum. Therefore, the kinetic energy is highest and the potential energy is lowest just before the object reaches the ground. However, the sum of potential energy and kinetic energy remains the same at all points, illustrating the law of conservation of energy.

Potential Energy + Kinetic Energy = Constant

or

mgh + 1/2 mv² = constant

The law of conservation of energy applies in all scenarios and for all types of transformations.

Try yourself:Water stored in a dam possesses

• A.no energy
• B.electrical energy
• C.kinetic energy
• D.potential energy

The diagram below shows a pendulum, which consists of a mass (m) connected to a fixed pivot point via a string of length (L).

Positions of the Pendulum

• At the highest point (A): Here, the pendulum is briefly at rest, and all its energy is potential energy (PE). The height (h) of the mass above the lowest point determines how much potential energy it has. The potential energy can be calculated using the formula: PE = m · g · h, where g is the acceleration due to gravity.
• At the lowest point (B): As the pendulum swings down, its potential energy is changed into kinetic energy (KE). At this point, its height (h) is zero, meaning it has no potential energy. Here, all its energy is kinetic energy, and the pendulum is moving at its highest speed. The kinetic energy can be calculated using the formula: KE = ½ m · v², where v is the velocity of the mass.
• At the highest point on the other side (C): As the pendulum swings upwards, its kinetic energy is transformed back into potential energy.

The total mechanical energy of the pendulum, which is the sum of kinetic energy and potential energy, stays the same throughout its motion. This shows the law of conservation of energy, which states that energy cannot be created or destroyed; it can only be changed from one form to another.

In essence, the energy changes in a pendulum illustrate that the total mechanical energy remains constant, confirming that the total energy before and after the change is unchanged.

Rate of Doing Work or Power

The rate at which work is done or energy is transferred is known as Power. Power indicates how quickly or slowly work is performed. The formula for calculating power is:

Power = Work done / Time taken

• The SI unit of power is a watt (W). One watt is defined as the power of an agent that does work at the rate of 1 joule per second (1 W = 1 J/s).
• We use larger units for energy transfer, such as kilowatts (kW): 1 kilowatt = 1 kW = 1000 watts.
• Other common units of power include:
  • 1 megawatt (MW) = 10⁶ watts
  • 1 horsepower (hp) = 746 watts

Average Power

Understanding average power is important because it helps us see how quickly work is done over time, even if that speed changes. You can calculate average power by dividing the total energy used by the total time taken. This results in a single number that shows the overall power, regardless of variations in the work rate.

• Average Power = Total energy consumed (or total work done) / Total time
• The power of a person can change over time, meaning they might work at different speeds during various intervals.

According to the law of conservation of energy, energy can only change forms; it cannot be created or destroyed. The total energy before and after any change always remains constant. Energy exists in various forms in nature, such as kinetic energy, potential energy, heat energy, and chemical energy. The total of kinetic and potential energies in an object is referred to as its mechanical energy.

Try yourself:A machine does 18000 Joules of work in 3 minutes. What is the average power of the machine in watts?

• A.300 W
• B.600 W
• C.100 W
• D.900W

What is Gravitation?

The force responsible for objects falling towards Earth, the Moon orbiting Earth, and planets orbiting the Sun. Isaac Newton identified this as the universal gravitational force.

• Newton’s Insight: Newton hypothesised that the same force that causes an apple to fall also keeps the Moon in orbit around Earth. This force acts towards the centre, known as the centripetal force.

Centripetal Force

Centripetal force is what keeps objects moving in a circular path. It pulls objects towards the centre of the circle, helping them keep moving in that circular motion. 

The Moon’s motion around Earth is due to the centripetal force provided by Earth’s gravitational attraction. Without this force, the Moon would move in a straight line.

Newton’s Third Law

• The Earth attracts an apple, and the apple attracts the Earth with an equal force (Newton’s Third Law).
• Due to the Earth’s significantly larger mass, its acceleration towards the apple is negligible, so we don’t observe the Earth moving towards the apple or the Moon.

Examples of Centripetal Force

Universal Law of Gravitation

According to Newton’s law of gravitation, the force of gravitational attraction between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. 

This means:

• The gravitational force gets weaker as you go higher up.
• It also changes on the Earth’s surface, becoming weaker from the poles to the equator.

Formula: If M and m are the masses of two objects separated by a distance d, the gravitational force of attraction between them is given by: 
F = G ^{M m}⁄_d²

where G is a constant, known as the Universal constant of gravitation.

• The universal constant of gravitation G is numerically equal to the force of attraction between two objects of unit mass each separated by unit distance.
• The value of G is 6.673 x 10^-11 N m² kg^-2.  This value was determined by Henry Cavendish (1731 – 1810) using a sensitive balance.
• G is called a universal constant because its value does not depend on the nature of the intervening medium or temperature, or other physical conditions
• As the value of G is extremely small, the gravitational force between regular objects is so small that it cannot be detected. 
• However, the force of attraction acting on an object due to Earth, the force of attraction between Earth and the moon, and the force experienced by planets due to the gravitational attraction of the Sun can be easily felt and measured.

Try yourself:Which of the following statements is true according to the universal law of gravitation?

• A.The force of attraction between two objects depends on their masses and the distance between them.
• B.The value of the universal constant of gravitation depends on the nature of the intervening medium.
• C.The gravitational force between ordinary terrestrial objects is easily detected and measured.
• D.The value of the universal constant of gravitation is 9.8 m/s².

Example 1: Suppose we have two objects: Object A with a mass of 5 kilograms and Object B with a mass of 10 kilograms. The distance between the centres of these objects is 2 meters. We’ll assume the gravitational constant, G, to be approximately 6.674 × 10^-11 N m²/kg².

Solution: 

Using the Universal Law of Gravitation, we can calculate the gravitational force between these objects:

F = (G * (m¹ * m²)) / r²

F = (6.674 × 10^-11 N m²/kg² * (5 kg * 10 kg)) / (2 m)²

F = (6.674 × 10^-11 N m²/kg² * 50 kg²) / 4 m²

F ≈ 8.3425×10 ⁻¹⁰N

Therefore, the gravitational force between Object A and Object B is approximately 8.3425×10 ⁻¹⁰ Newtons.

Importance Of The Universal Law Of Gravitation

The universal law of gravitation explains various phenomena that were once thought to be unrelated:

• The force that keeps us grounded on Earth
• The moon’s orbit around the Earth
• This same force governs the planets’ movement around the Sun
• The tides caused by the moon and the Sun

Free Fall or Gravity

The force that pulls objects toward the Earth is known as the force of gravity.

• For an object with mass m located on or near the Earth, this force can be calculated using the formula: F = GMm/R², where G is the universal gravitational constant, M is the mass of the Earth, and R is the radius of the Earth.
• The acceleration produced in a freely falling object on account of the force of gravity is known as the acceleration due to gravity. It is denoted by the symbol ‘g’.

Gravitation Formula

To calculate the Value of g

The acceleration due to gravity at Earth’s surface is given by the formula: g = GM/R². The average value of g on the surface of the Earth is about 9.8 m/s². To find g, we use these constants:

• G = 6.7 × 10^-11 N m²/kg² (Gravitational Constant)
• M = 6 × 10 ²⁴ kg (Mass of the Earth) 
• R = 6.4 × 10⁶ m (Radius of the Earth) 
• Here’s how the value of g is calculated.

Calculation of acceleration due to gravity

The motion of Objects under the influence of the Gravitational Force of the Earth

The value of g varies from place to place. On the surface of the earth value of g is more at the poles than at the equator. The value of g also decreases as one moves farther from the Earth.

Free Fall Motion

• When an object falls towards the Earth under the force of gravity alone, we say that the object is in free fall. A freely falling object experiences a constant acceleration of g (=9.8ms^-2) during its downward motion. 
• However, if an object is projected vertically upward with a certain velocity, its velocity goes on decreasing due to gravity, till it comes to rest and then starts falling vertically downward under gravity.
• To demonstrate the impact of air resistance on falling objects, try this activity:Activity: Drop a piece of paper and a stone from the same height at the same time. Check if both hit the ground together. You will notice that the paper takes longer to fall because of air resistance. In a vacuum, both would fall at the same speed.
• The three equations of motion, viz, (i) v = u + at, (ii) s = ut + 1/2 at²,  and (iii) v² – u² = 2as, are true for the motion of objects under gravity. For free fall, the value of acceleration a = g = 9.8ms^-2.
• If an object is just let fall from a height, then in that case u = 0 and a = +g = +9.8ms^–2.
• If an object is projected vertically upwards with an initial velocity u, then a = -g = -9.8ms^-2 and the object will go to a maximum height h where its final velocity becomes zero (i.e. v = 0). In such a case 

Examples for the Three Equations of Motion Under Gravity

1. Using v = u+at:

2. Using s = ut + 1/2at²

2. Using v²−u²=2as:

Mass

The mass of an object is a measure of its inertia. The mass of an object is constant and does not change from place to place. Greater mass means greater inertia, resisting changes in motion.

Mass and Weight

Weight

• The weight of an object is the force with which it is attracted towards the Earth. The weight W of an object of mass m will be W = mg. Weight is a force acting vertically downwards. It means that it is a vector.
• As the weight of an object is a force, its SI unit is Newton (N).
  An object of mass m = 1 kg has thus a weight of W = 1 x 9.8 = 9.8 N.
• At a given place weight of an object is directly proportional to its mass, i.e,  (at a given place). For this reason, at a given place, we may use the weight of an object as a measure of its mass.

Weight of Object on the Moon

• The mass of an object stays the same no matter where it is. This is important for understanding the difference between mass and weight. Weight is the force that pulls an object towards the Earth or the Moon.
• The force of gravity due to the moon is 1/6th of the force of gravity due to Earth.
  Hence 
  Due to this very reason weight of an object on the moon will be 1/6th of its weight on Earth.

Try yourself:Question: Which of the following statements about weight is true?

• A.Weight is a measure of the amount of matter in an object.
• B.Weight is the force of gravity acting on an object.
• C.Weight is a constant property of an object and does not change.
• D.Weight is the same as mass.

Thrust and Pressure

The normal force acting on a surface, due to the weight of an object placed on the surface, is called ‘thrust’. As thrust is a sort of force hence its SI unit is “a newton” (N).

Thrust

• The thrust on unit surface area is called pressure.
  Pressure 
  Thus, pressure on a given object is the normal force acting on its surface per unit surface area.
  SI unit of pressure is N m^-2, but it is also called pascal and denoted by the symbol Pa.
  ∴ 1 pascal (1 Pa) = 1 N m^-2 
• The same force acting on a smaller area exerts a larger pressure. It is due to this reason that a nail or a pin has a pointed tip, and knives have sharp edges.
• Given force acting on a larger area exerts a smaller pressure. It is due to this reason that the foundations of houses are made broad, the base of dams is made broad, sleepers are laid below the railway line and so on.

Pressure in Fluids

Fluid is that state of matter which can flow. All liquids and gases are fluids.

• Fluids have weight and exert pressure on the base and walls of their container.
• Any pressure in a confined fluid is transmitted equally in all directions.
• The SI unit of pressure is the pascal, abbreviated as Pa.

Also read: Short & Long Answer Questions- Gravitation

Buoyancy

• When an object is placed in a fluid, it feels a force pushing it upwards, known as upthrust or buoyant force. All objects experience this force when submerged in a fluid.
• The strength of the buoyant force depends on the fluid’s density, causing the object to rise when released.

Buoyancy

Try yourself:What is the SI unit of weight?

• A.Newton (N)
• B.Kilogram (kg)
• C.Pascal (Pa)
• D.Meter (m)

Why Objects Float Or Sink When Placed On The Surface Of Water?

The ability of an object to float or sink in water depends on its density compared to the water’s density and the buoyant force acting on it. Density measures how much mass is in a certain volume.

Floating and Sinking on Surface of Water

When an object is placed in water, it experiences two main forces: buoyancy and gravity.

• Buoyancy is the upward force on an object in a fluid, like water. This force arises from the pressure difference on the object’s top and bottom. According to Archimedes’ principle, the upward buoyant force equals the weight of the water displaced by the object. The more water the object displaces, the greater the buoyant force. If the object’s weight exceeds the buoyant force, it will sink; if the buoyant force is greater, it will float.
• The weight of an object is the result of its mass multiplied by the acceleration due to gravity. While weight can change depending on location, the mass remains constant.

In summary, whether an object floats or sinks in water depends on the comparison between its weight and the buoyant force exerted by the water. If the object’s weight is greater, it will sink. If the buoyant force is greater, it will float.

Archimedes’ Principle

A Greek scientist Archimedes found a principle about buoyant force, which is the reduction in weight of an object when it is placed in a fluid. He realised this after he saw water spill from a bathtub when he got in. He ran through the streets shouting “Eureka!”, which means “I have found it”.

Archimedes’ Principle

• According to Archimedes’ principle, “when an object is fully or partially placed in a fluid, it feels an upward force equal to the weight of the fluid it displaces.”
• This principle has many uses, like in designing ships and submarines. It is also the basis for lactometers, which check the purity of milk, and hydrometers, which measure the density of liquids.

Try yourself:Archimedes’ principle states that:

• A.The buoyant force on an object is equal to the weight of the fluid displaced by the object
• B.The buoyant force on an object is equal to the volume of the fluid displaced by the object
• C.The buoyant force on an object is equal to the mass of the fluid displaced by the object
• D.The buoyant force on an object is equal to the density of the fluid displaced by the object

Introduction to Motion and Force

Motion is  described in terms of position, velocity, and acceleration. Motion can be uniform (consistent speed) or non-uniform (changing speed).Historical Perspective:

• Ancient Belief: Objects at rest are in their “natural state.”
• Galileo & Newton: Challenged the old belief, developing new understanding of motion and its causes.

A force is an effort that changes the state of an object at rest or at motion. It can change an object’s direction and velocity. Force can also change the shape of an object.

It is the force that enables us to do any work.
To do anything, either we pull or push the object. Therefore, pull or push is called force.
Example: To open a door, either we push or pull it. A drawer is pulled to open and pushed to close. 

Push or Pull is called Force

Effects of Force

• Force can make a stationary body move.
• Force can stop a moving body.
• Force can change the direction of a moving object.

Effects of Force

• Force can change the speed of a moving body.
• Force can change the shape and size of an object.

Try yourself:Which of the following statements best defines force?

• A.Force is the effort that changes the state of an object at rest or in motion.
• B.Force is the energy that enables us to do any work.
• C.Force is the push or pull applied to an object.
• D.Force is the ability to change the direction and velocity of an object.

Balanced and Unbalanced Forces

In physics, forces can be classified as balanced or unbalanced based on their effects on an object’s motion. Mentioned below are the details of both these forces: 

Balanced and Unbalanced Forces

Balanced Forces

If the resultant of applied forces is equal to zero, it is called balanced forces.

Balanced Force

• Example: In the tug of war if both teams apply similar magnitude of forces in opposite directions, the rope does not move in either side. This happens because of balanced forces in which the resultant of applied forces becomes zero.
• Balanced forces do not cause any change in the state of an object. Balanced forces are equal in magnitude and opposite in direction.
• Balanced forces can change the shape and size of an object.
  Example: When forces are applied from both sides over a balloon, the size and shape of the balloon are changed.

Unbalanced Forces

If the resultant of applied forces are greater than zero, the forces are called unbalanced forces. An object at rest can be moved because of applying unbalanced forces.

Unbalanced Force

Unbalanced forces can do the following:

• Move a stationary object.
• Increase the speed of a moving object.
• Decrease the speed of a moving object.
• Stop a moving object.
• Change the shape and size of an object.

Newton’s Laws of Motion

Newton studied the ideas of Galileo and gave the three laws of motion. These laws are known as Newton’s laws of motion:
(i) Newton’s First Law of Motion (Law of Inertia).
(ii) Newton’s Second Law of Motion.
(iii) Newton’s Third Law of Motion.

First Law of Motion (Law of Inertia)

Any object remains in the state of rest or uniform motion along a straight line until it is compelled to change the state by applying an external force.

Illustration of Newton’s First Law of Motion

Explanation

• If any object is in the state of rest, then it will remain in rest until an external force is applied to change its state.
• Similarly, an object will remain in motion until an external force is applied over it to change its state.
• This means all objects resist changing their state. The state of any object can be changed by applying external forces only. 

Examples of Newton’s First Law of Motion in Everyday Life

• A person standing inside a bus falls backwards when the bus starts moving suddenly.
  Explanation: This happens because the person and bus both are at rest while the bus is not moving, but as the bus starts moving, the legs of the person start moving along with the bus, but the rest portion of his body has the tendency to remain in rest. Because of this, the person falls backwards; if he is not alert.
• A person standing inside a moving bus falls forward if the driver applies brakes suddenly.
  Explanation: This happens because when the bus is moving, the person standing in it is also in motion along with the bus. But when the driver applies brakes the speed of the bus decreases suddenly or the bus comes into a state of rest suddenly, in this condition the legs of the person, which are in contact with the bus come to rest while the rest part of his body tends to remain in motion. Because of this person falls forward if he is not alert.
• Before hanging the wet clothes over the laundry line, usually, many jerks are given to the clothes to get them dried quickly. Because of jerks, droplets of water from the pores of the cloth fall on the ground, and a reduced amount of water in clothes dries them quickly.
  Explanation: This happens because when suddenly clothes are made in motion by giving jerks, the water droplets in them have the tendency to remain at rest and they are separated from the clothes and fall on the ground.
• When a striker hits the pile of coins on the carom-board, the coin only at the bottom moves away leaving the rest of the pile of the coin in the same place.
  Explanation: This happens because when the pile is struck with a striker, the coin at the bottom comes in motion while the rest of the coin in the pile has the tendency to remain in the rest and they vertically fall on the carom-board and remain at the same place.

Galileo’s Idea of Motion

Galileo first said that objects move at a constant speed when no forces act on them.

Galileo’s Idea of Motion

• This means if an object is moving on a frictionless path and no other force is acting upon it, the object will be moving forever. That is, there is no unbalanced force working on the object.
• But practically it is not possible for any object. Because to attain the condition of zero, the unbalanced force is impossible.
• Force of friction, Force of air, and many other forces are always acting upon an object.

Inertia and Mass

• The property of an object because of which it resists getting disturbed in its state is called inertia.
  In other words, the natural tendency of an object that resist the change in the state of motion or rest of the object is called inertia.
• The inertia of an object is measured by its mass. Inertia is directly proportional to the mass of the object.

Inertia increases with an increase in mass and decreases with a decrease in mass.

• A heavy object will have more inertia than the lighter one.
  Since a heavy object has more inertia, thus it is more difficult to push or pull a heavy box over the ground than the lighter one. 
• Inertia is the natural tendency of an object to resist a change in its state of motion or of rest. The mass of an object is a measure of its inertia. 

Try yourself:

Which of the following statements best describes a balanced force?

• A.A force that can change the shape and size of an object.
• B.A force that can stop a moving object.
• C.A force that can move a stationary object.
• D.A force that does not cause any change in the state of an object.

Second Law of Motion 

The rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of the force.

Illustration of Force depending on Mass and Acceleration

(a) Momentum

• Momentum is the power of motion of an object.
• The product of velocity and mass is called momentum.
  Momentum is denoted by ‘p’.
• Therefore, Momentum of the object = Mass × Velocity (p = m × v),
  where p = momentum, m = mass of the object and v = velocity of the object. 

 Some explanations to understand the momentum:

• A person gets injured in the case of hitting a moving object, such as a stone, pebbles, or anything because of the momentum of the object.
• Even a small bullet can kill a person when it is fired from a gun because of its momentum due to great velocity.
• A person gets injured severely when hit by a moving vehicle because of the momentum of the vehicle due to mass and velocity.

(b) Momentum and Mass

• Since momentum is the product of mass and velocity (p = m × v) of an object. This means momentum is directly proportional to mass and velocity. Momentum increases with the increase of either the mass or velocity of an object.
• This means if a lighter and a heavier object is moving with the same velocity, then the heavier object will have more momentum than the lighter one.
• If a small object is moving with great velocity, it has tremendous momentum. And because of momentum, it can harm an object more severely.Example: A small bullet having a small mass even kills a person when it is fired from a gun.
• Usually, road accidents prove more fatal because of high speed than slower speed. This happens because vehicles running at high speed have greater momentum compared to a vehicles running at a slower speed.

(c) Unit of Momentum

• We know that,
  Momentum (p) = m × v
• SI unit of mass = kg
• SI unit of velocity = m/s

Therefore,

p = kg × m/s ⇒ p = kgm/s 

The momentum of an object which is in the state of rest:
Let, an object with mass ‘m’ be in the rest.
Since, the object is at rest, therefore, its velocity, v = 0
∵ Momentum = mass × velocity
⇒ p = m × 0 = 0
Thus, the momentum of an object in the rest, i.e. non-moving is equal to zero.

Numerical Problems Based on Momentum 

Example 1: What will be the momentum of a stone that has a mass of 10 kg when it is thrown with a velocity of 2 m/s?
Solution: Mass (m) = 10 kg, Velocity (v) = 2 m/s.
∵ Momentum (p) = Mass (m) × Velocity (v)
⇒ p = 10 kg × 2 m/s = 20 kg m/s.
Thus, the momentum of the stone = 20 kg m/s.

Example 2: Calculate the momentum of a bullet of 25 g when it is fired from a gun with a velocity of 100 m/s.
Solution: Given the velocity of the bullet (v) = 100 m/s,
Mass of the bullet (m) = 25 g = 25/1000 kg = 0.025 kg.
∵ p = m × v
⇒ p = 0.025 × 100 = 2.5 kg m/s.
Thus, the Momentum of the bullet  = 2.5 kg m/s.

Example 3: Calculate the momentum of a bullet having a mass of 25 g is thrown using a hand with a velocity of 0.1 m/s.
Solution: Given the velocity of the bullet (v) = 0.1 m/s,
Mass of the bullet (m) = 25 g = 25/1000 kg = 0.025 kg.
∵ Momentum (p) = Mass (m) × Velocity (v)
⇒ p = 0.025 kg × 0.1 = 0.0025 kg m/s
Thus, Momentum of the bullet = 0.0025 kg m/s.

Example 4: The mass of a goods lorry is 4000 kg and the mass of goods loaded on it is 20000 kg. If the lorry is moving with a velocity of 2 m/s, what will be its momentum?
Solution: Velocity (v) = 2 m/s
⇒ Mass of lorry = 4000 kg
⇒ Mass of goods on the lorry = 20000 kg.
⇒ Total mass (m) on the lorry = 4000 kg + 20000 kg = 24000 kg
∵ Momentum (p) = Mass (m) × Velocity (v)
⇒ p = 24000 kg × 2 = 48000 kg m/s
Thus, the Momentum of the lorry = 48000 kg m/s.

Example 5: A car having a mass of 1000 kg is moving with a velocity of 0.5 m/s. What will be its momentum?
Solution: Velocity of the car (v) = 0.5 m/s
⇒ Mass of the car (m) = 1000 kg.
∵ Momentum (p) = Mass (m) × Velocity (v)
⇒ p = 1000 kg × 0.5 m/s = 500 kg m/s
Thus, the Momentum of the car = 500 kg m/s.

Mathematical Formulation of the Second Law of Motion

Suppose the mass of an object = m kg
Initial velocity of an object = u m/s,
The final velocity of an object = v m/s.
Initial momentum, p₁ = mu, Final momentum, p₂ = mv.
Change in momentum = Final momentum – Initial momentum
Change in momentum = mv – mu = m(v – u)
Rate of change of momentum = Change in momentum/Time taken
Rate of change of momentum = m(v-u)/t

According to 2nd law, this rate of change is momentum is directly proportional to force, i.e.

Newton’s Second Law of MotionWe know that:
a = (v-u)/t (From 1st equation of motion)
⇒ F = kma, where k is a constant.
Its value can be assumed as 1.
⇒ F = 1 × m × a = ma

SI unit = kgms^-2 or Newton

1 Newton: When an acceleration of 1 m/s² is seen in a body of mass 1 kg, then the force applied on the body is said to be 1 Newton.

Proof of Newton’s First Law of Motion from the Second Law
The first law states that if external force F = 0, then a moving body keeps moving with the same velocity, or a body at rest continues to be at rest.
⇒ F = 0
We know, F = m(v-u)/t

• A body is moving with initial velocity u then,
  m(v-u)/t = 0 ⇒ v – u = 0
  ⇒ v = u
  Thus, the final velocity is also the same.
•  A body is at rest i.e., u = 0
  ⇒ u = v = 0
  Hence, the body will continue to be at rest.

Try yourself:Which of the following statements is true about momentum?

• A.Momentum is the product of mass and acceleration.
• B.Momentum is directly proportional to mass of the object.
• C.Momentum is the product of force and time.
• D.Momentum is the rate of change of velocity of an object.

Third Law of Motion

• According to Newton’s Third Law of Motion, for every action, there is an equal and opposite reaction.
• Newton’s Third Law of Motion explains the interaction between two objects when a force is applied.
• Action and Reaction Forces:
  – When one object exerts a force on another, the second object exerts an equal and opposite force back on the first.
  – These forces are equal in magnitude but opposite in direction.
  – These forces act on different objects, never on the same object.
• Example:
  Gun Recoil:– When a gun is fired, it exerts a forward force on the bullet.
  – The bullet exerts an equal and opposite force on the gun, causing it to recoil.
  – The gun’s greater mass results in less acceleration compared to the bullet.

Illustration of 3rd Law of Motion.

Applications

• Walking is enabled by the 3rd law.
• A boat moves back when we deboard it.
• A gun recoils.
• Rowing of a boat.

In our daily lives, objects such as birds, fish, and cars can be either at rest or in motion. Motion is observed when an object’s position changes over time. Sometimes, motion is inferred indirectly, like noticing dust moving to deduce air movement. Perception of motion can vary: passengers in a moving bus see trees moving backward, while onlookers outside the bus see both the bus and its passengers in motion.

Motion

Describing Motion

To describe an object’s motion, we use a reference point, or origin, as a fixed location. For instance, if a school is 2 km north of a railway station, the railway station is the reference point. This origin helps us measure and describe the object’s position relative to it.

What is Motion?

A body is said to be in a state of motion when its position changes continuously with reference to a point. Motion can be of different types depending upon the type of path by which the object is travelling through:

Types of Motion

• Circulatory motion/Circular motion: In a circular path.
• Linear motion: In a straight-line path.
• Oscillatory/Vibratory motion: To and fro path with respect to origin.

Motion Along a Straight Line

The simplest type of motion is along a straight line. 
Let’s understand this with an example. Imagine an object moving along a straight path, starting from point O, which we use as the reference point.

Motion along a straight line

Example Description

• Initial Motion: The object starts at point O and moves to point A via points C and B.
• Return Motion: The object then travels back from A to C through B.

Distance Covered

The total path length covered by the object is the sum of the distances traveled:

• Distance from O to A: 60 km
• Distance from A to C: 35 km
• Total Distance from O to C = OA + AC = 60 km + 35 km = 95 km

Distance is a scalar quantity, meaning it only has magnitude and no direction.

• Scalar quantity: It is the physical quantity having its own magnitude but no direction.
  Example: Distance, Speed.
• Vector quantity: It is the physical quantity that requires both magnitude and direction.
  Example: Displacement, Velocity.

Distance and Displacement

1. Distance

The actual path of length travelled by an object during its journey from its initial position to its final position is called the distance.

• Distance is a scalar quantity that requires only magnitude but no direction to explain it.
• Example: Ramesh travelled 65 km. (Distance is measured by odometer in vehicles.)

2. Displacement

The shortest distance travelled by an object during its journey from its initial position to its final position is called displacement.

• Displacement is a vector quantity requiring both magnitude and direction for its explanation.
• Example: Ramesh travelled 65 km southwest from Clock Tower.
• Displacement can be zero (when the initial point and final point of motion are the same)
  Example: Circular motion.

Example of Zero Displacement

Try yourself:What is the definition of distance?

• A.A body is said to be in a state of rest when its position does not change with respect to a reference point.
• B.A body is said to be in a state of motion when its position changes continuously with reference to a point.
• C.The actual path of length travelled by an object during its journey from its initial position to its final position.
• D.The physical quantity that requires both magnitude and direction.

Example 1: A body travels in a semicircular path of radius 10 m starting its motion from point ‘A’ to point ‘B’. Calculate the distance and displacement.

Sol. Given, π = 3.14, R = 10 m

The distance is the length of the semicircular path.

Distance = Circumference of a circle ÷ 2 

Distance = 2πR ÷ 2 

Distance = πR 
= 3.14 × 10 = 31.4 m

Where as , 

Displacement = 2 × R = 2 × 10 = 20 m

Example 2: A body travels 4 km towards North then he turns to his right and travels another 4 km before coming to rest. Calculate 

(i) total distance travelled, 

(ii) total displacement.

Sol. The total distance is the sum of all the paths travelled:

Total Distance = 4km (North) + 4km (Right) = 8km

Since displacement is the shortest straight-line distance between the starting point and the final point.

The path forms a right triangle, where:

• One leg = 4 km (North direction),
• Other leg = 4 km (Right direction).

Try yourself:What is the difference between distance and displacement?

• A.Distance is a vector quantity, while displacement is a scalar quantity.
• B.Distance requires both magnitude and direction, while displacement only requires magnitude.
• C.Distance is measured in kilometers, while displacement is measured in meters.
• D.Distance is the actual path traveled by an object, while displacement is the shortest distance between the initial and final positions.

Uniform and Non-uniform Motion

1. Uniform Motion

• When a body travels equal distances in equal intervals of time, then the motion is said to be a uniform motion.

2. Non-uniform Motion

• In this type of motion, the body travels unequal distances in equal intervals of time.
• Two types of non-uniform motion:
  (i) Accelerated Motion: When the motion of a body increases with time.
  (ii) De-accelerated Motion: When the motion of a body decreases with time.

Measuring the Rate of Motion

The measurement of distance travelled by a body per unit of time is called speed.
i.e. Speed (v) = Distance Travelled/Time Taken = s/t

• SI unit: m/s (meters/second)
• If a body is executing uniform motion, then there will be a constant speed.
• If a body is travelling with a non-uniform motion, then the speed will not remain uniform but have different values throughout the motion of such a body.
• For non-uniform motion, the average speed will describe one single value of speed throughout the motion of the body.
  i.e. Average speed = Total distance travelled/Total time taken

Conversion Factor
Change from km/hr to m/s = 1000m/(60×60)s = 5/18 m/s

Example: What will be the speed of body in m/s and km/hr if it travels 40 km in 5 hrs?
Sol: Distance (s) = 40 km
Time (t)  = 5 hrs.
Speed (in km/hr) = Total distance/Total time = 40/5 = 8 km/hr
40 km = 40 × 1000 m = 40,000 m
5 hrs = 5 × 60 × 60 sec.
Speed (in m/s) = (40 × 1000)/(5×60 ×60) = 80/36 = 2.22 m/s

Speed with Direction

• It is the speed of a body in a given direction.
• The measurement of displacement travelled by a body per unit of time is called velocity.
  i.e. Velocity = Displacement/Time
• SI unit of velocity: ms^-1
• Velocity is a vector quantity. Its value changes when either its magnitude or direction changes.
• It can be positive (+ve), negative (-ve) or zero.
• For non-uniform motion in a given line, average velocity will be calculated in the same way as done in average speed.
  i.e. Average velocity = Total displacement/Total time
• For uniformly changing velocity, the average velocity can be calculated as follows:-

Avg. Velocity (v_avg) = (Initial velocity + Final velocity)/2 = (u+v)/2
where,  u = initial velocity, v = final velocity 

Example 1: During the first half of a journey by a body it travels with a speed of 40 km/hr and in the next half it travels at a speed of 20 km/hr. Calculate the average speed of the whole journey.

Sol: The average speed for a journey where the distances are equal but the speeds are different is not simply the arithmetic mean 

When a body covers equal distances at different speeds, the correct formula for average speed is:
Given:

• Speed during the first half (v1) = 40 km/hr
• Speed during the second half (v2) = 20 km/hr

Now, use the correct formula:

Example 2: A car travels 20 km in first hour, 40 km in second hour and 30 km in third hour. Calculate the average speed of the vehicle.

Sol: Speed in 1st hour = 20 km/hr

Distance travelled during 1st hr = 1 × 20= 20 km

Speed in 2nd hour = 40 km/hr

Distance travelled during 2nd hr = 1 × 40= 40 km

Speed in 3rd hour = 30 km/hr

Distance travelled during 3rd hr = 1 × 30= 30 km

Average speed = Total distance travelled/Total time taken

= (20 + 40 + 30)/3 = 90/3 = 30 km/hr

Try yourself:What is the definition of uniform motion?

• A.When a body travels unequal distances in equal intervals of time.
• B.When a body travels equal distances in equal intervals of time.
• C.When the motion of a body increases with time.
• D.When the motion of a body decreases with time.

Rate of Change of Velocity

• Acceleration is seen in non-uniform motion and it can be defined as the rate of change of velocity with time.
  i.e. Acceleration (a) = Change in velocity/Time = (v-u)/t
  where, v = final velocity, u = initial velocity
• Here, v > u, then ‘a’ will be positive (+ve). If v is greater than u, then acceleration (a) will be positive.
  

Example: A car speed increases from 40 km/hr to 60 km/hr in 5 sec. Calculate the acceleration of car.
Sol. u = 40km/hr = (40×5)/18 = 100/9 = 11.11 m/s
v  = 60 km/hr = (60×5)/18 = 150/9 = 16.66 m/s
t = 5 sec
a = (v-u)/t = (16.66 – 11.11)/5 = 5.55/5 = 1.11 ms^-2

Try yourself:Which quantity requires both magnitude and direction.

• A.Distance
• B.Displacement
• C.Speed
• D.None of these

Retardation/Deceleration

• Deceleration is seen in non-uniform motion during decrease in velocity with time. It has same definition as acceleration.
  i.e. Deceleration (a’) = Change in velocity/Time = (v-u)/t
• Here, v < u, ‘a’ = negative (-ve).

Example: A car travelling with a speed of 20 km/hr comes into rest in 0.5 hrs. What will be the value of its retardation?
Sol. v = 0 km/hr, u = 20 km/hr, t = 0.5 hrs
Retardation, a = (v-u)/t = (0-20)/0.5 = -200/5 = -40 km hr^-2

Graphical Representation of Motion

1. Distance-Time Graph (s/t graph)

(i) s/t graph for uniform motion:
(ii) s/t graph for non-uniform motion:

(iii) s/t graph for a body at rest:
v = (s₂ – s₁)/(t₂ – t₁)
But, s₂ – s₁
∴ v = 0/(t₂ – t₁) or v = 0

2. Velocity-Time Graph (v/t graph)

(i) v/t graph for uniform motion:
a = (v₂ – v₁)/(t₂ – t₁)
But, v₂ – v₁
∴ a = 0/(t₂ – t₁) or a = 0
(ii) v/t graph for uniformly accelerated motion:

In uniformly accelerated motion, there will be an equal increase in velocity in equal intervals of time throughout the motion of the body.
(iii) v/t graph for non-uniformly accelerated motion:
a₂ ≠ a₁
(iv) v/t graph for uniformly decelerated motion:
a₁‘ = a₂‘
(v) v/t graph for non-uniformly decelerated motion:

Note: In v/t graph, the area enclosed between any two time intervals, t₂ – t₁, will represent the total displacement by that body.

The displacement can also be calculated as the area of the trapezium formed by the v/t graph:

= Area of ∆ABC + Area of rectangle ACDB = ½ × (v₂ – v₁)×(t₂ – t₁) + v₁× (t₂ – t₁)

Example: From the information given in the s/t graph, which of the following body ‘A’ or ‘B’ will be faster?
Sol. v_A > v_B

Try yourself:Which of the following statements is true about acceleration?

• A.Acceleration is only seen in uniform motion.
• B.Acceleration is the rate of change of velocity with time.
• C.Acceleration is always negative.
• D.Acceleration is the rate of change of distance with time.

Equations of Motion by Graphical Method

Also read: NCERT Solutions: Motion

1. First Equation: v = u + at

Final velocity = Initial velocity + Acceleration × Time
Graphical Derivation
Suppose a body has initial velocity ‘u’ (i.e., velocity at time t = 0 sec.) at point ‘A’ and this velocity changes to ‘v’ at point ‘B’ in ‘t’ secs. i.e., final velocity will be ‘v’.

For such a body there will be an acceleration. a = Change in velocity/Change in Time
⇒ a = (OB – OA)/(OC-0) = (v-u)/(t-0)
⇒ a = (v-u)/t
⇒ v = u + at

2. Second Equation: s = ut + ½ at2

Distance travelled by object = Area of OABC (trapezium)
= Area of OADC (rectangle) + Area of ∆ABD
= OA × AD + ½ × AD × BD
= u × t + ½ × t × (v – u)
= ut + ½ × t × at  
⇒ s = ut + ½ at²  (∵a = (v-u)/t)

3. Third Equation: v² = u² + 2as

s = Area of trapezium OABC


Example 1: A car starting from rest moves with a uniform acceleration of 0.1 ms^-2 for 4 mins. Find the speed and distance travelled.
Sol: u = 0 ms^-1 (∵ car is at rest), a = 0.1 ms^-2, t = 4 × 60 = 240 sec.
v = ?
From, v = u + at
v = 0 + (0.1 × 240) = 24 ms^-1

Example 2: The brakes applied to a car produces a deceleration of 6 ms ^-2 in the opposite direction to the motion. If a car requires 2 sec. to stop after the application of brakes, calculate the distance travelled by the car during this time.
Sol: Deceleration, a = − 6 ms^-2; Time, t = 2 sec.
Distance, s =?
Final velocity, v = 0 ms^-1 (∵ car comes to rest)
Now, v = u + at
⇒ u = v – at = 0 – (-6×2) = 12 ms-¹
s = ut + ½ at² = 12 × 2 + ½ (-6 × 2²) = 24 – 12 = 12 m

Try yourself:A car is moving with an initial velocity of 20 m/s. If it accelerates at a rate of 5 m/s? for 4 seconds, what is its final velocity?

• A.15 m/s
• B.40 m/s
• C.35 m/s
• D.45 m/s

Uniform Circular Motion

• If a body is moving in a circular path with uniform speed, then it is said to be executing the uniform circular motion.
• In such a motion the speed may be the same throughout the motion but its velocity (which is tangential) is different at each and every point of its motion. Thus, uniform circular motion is an accelerated motion.
• Direction at different points while executing circular motion