th CBSE PHYSICS Gravitation Class IX

th CBSE PHYSICS Gravitation Class IX

Science CBSE Physics Flotation Term-II Class IX Force :

Pressure :Thrust :Atmospheric pressure: Buoyant force

Thrust The force acting on a body perpendicular to its surface is called thrust.The S.I. unit of thrust is Newton (N).e.g. For fixing a poster on a bulletin board one has to press drawing pins with the thumb.

When pressing a drawing pin, force is applied on the surface area of its head.

The force is directed perpendicular to the surface of the board. This force is called thrust.Pressure The thrust per unit area is called pressure.Pressure = Thrust/ AreaThe S.I. unit of pressure is Newton per square metre (N/m2) which is also called pascal (Pa).

Many times a bigger unit of pressure called kilopascal (kPa) is used.The pressure depends on two factors:(a). Force applied (b). Area over which force acts.

The same force can produce different pressures depending on the area over which it acts

e.g. when a force acts over a large area of an object, it produces a small pressure.

But if the same force acts over a small area of the object, it produces a large pressure.Let we take two similar bricks lying on the ground, one in the lying position and another in the standing position. The two bricks exert the same force on the ground because they have the same weight.

But the two bricks exert different pressures on the ground because their areas in contact with the ground are different.

The brick in thelying position has a large areain contact with the ground. So, the force of the weight of the brick falls on a large area of the ground and the force per unit area or pressure on the ground is less.

The brick in thestanding positionhas a small area in contact with the ground. So, the force of the weight of the brick falls on a smaller area of the ground and the pressure on the ground is more.A school bag has wide straps made of thick cloth= The weight of bag may fall over a large area of the shoulder of the child producing less pressure on the shoulder. And due to less pressure, it is more comfortable to carry the heavy school bag.

= On the other hand, if the school bag has a strap made of thin string, then the weight of school bag will fall over a small area of the shoulder. This will produce a large pressure on the shoulder of the child and it will become very painful to carry the heavy school bag.A sharp knife cuts better than a blunt knife.A sharp knife hasa very thin edge to its blade.Due to its very thin edge, the force of our hand falls over a very small area of the object producing a large pressure. And this large pressure cuts the object easily.

On the other hand, a blunt knifedoes not cut an object easily because due to its thicker edge, the force of our hand falls over a larger area of the object and produces lesser pressure. This lesser pressure cuts the object with difficulty.

The tip of a sewing needle is sharpso that due to its sharp tip, the needle may put the force on a very small area of the cloth, producing a large pressure sufficient to pierce the cloth being stitched.The pressure on ground is more when a man is walking than when he is standing.

When a man is walking, then at one time only his one foot is on the ground.Due to this, the force of weight of man falls on a smaller area of the ground and produces more pressure on the ground.

On the other hand, when the man is standing, then both his feet are on the ground.Due to this the force of weight of the man falls on a larger area of the ground and produces lesser pressure on the ground.

The depression is much more when a man stands on the cushion than when he lies down on it.

When a man stands on a cushion then only his two feet (having small area) are in contact with the cushion. Due to this the weight of man falls on a small area of the cushion producing a large pressure. This large pressure causes a big depression in the cushion.

On the other hand, when the same man is lying on the cushion, then his whole body (having large area) is in contact with the cushion. In this case the weight of man falls on a much larger area of the cushion producing much smaller pressure. And this smaller pressure produces a very little depression in the cushion.

The tractors have broad tyresso that there is less pressure on the ground and the tyres do not sink into comparatively soft ground in the fields.

A wide steel belt is provided over the wheels of army tanks so that they exert less pressure on the ground and do not sink into it.

Wooden sleepers (or concrete sleepers) are kept below the railway lineso that there is less pressure of the train on the ground and railway line may not sink into the ground.

The snow shoes have large, flat solesso that there is less pressure on the soft snow and this stops the wearer from sinking into it.It is easier to walk on soft sand if we have flat shoes rather than shoes with small heels(or pencil heels). This is because a flat shoe has a greater area in contact with the soft sand due to which there is less pressure on the soft ground. Due to this the flat shoes do not sink much in soft sand and it is easy to walk on it.

On the other hand, a small heel (or sharp heel) has a small area is contact with the soft sandand so exerts a greater pressure on the soft sand. Due to this greater pressure, the small heels tend to sink deep into soft sand making it difficult for the wearer to walk on soft sand.

The foundations of buildings and dams are laid on a larger area of groundso that the weight of the building or dam (to be constructed) produces less pressure on ground and the building or dam may not sink into the ground. Atmospheric pressure The pressure at any place due to the atmosphere is called atmospheric pressure. Its value varies from place to place and also with the time.

Atmospheric pressure at the earths surface near the sea level is around 1.01x105 Pa. This value is known as 1atmosphere of pressure (1atmosphere = 760mm of Hg).Pressure in fluids All liquids and gases are fluids.

A solid exerts pressure on a surface due to its weight

Similarly, fluids have weight, and they also exert pressure on the base and walls of the container in which they are enclosed.

Pressure exerted in any confined mass of fluid is transmitted undiminished in all directions.

The pressure in a liquid is the same at all points at the same horizontal level. As we go deeper in the liquid, the pressure increases.

Buoyancy When an object is placed in a liquid, the liquid exerts an upward force on it e.g. When a piece of cork is held below the surface of water and then released the cork immediately rises to the surface.

It is a common experience that a mug filled with water appears to be heavier when it is lifted above the surface of water in a bucket.

In general, whenever an object is immersed in water, it appears to lose some weight and feels lighter. The weight of the object in water is called apparent weight. It is less than its true weight.

The objects appear to be less heavy when submerged in water because the water exerts an upward force on them.

The upward force acting on an object immersed in a liquid is called buoyant force. The buoyant force is also known as upthrust. It is due to the buoyant force exerted by the liquid that the weight of an object appears to be less in the liquid than its actual weight in air.

It is due to the buoyant force exerted by water that we are able to swim in water and ships float on water.

The tendency of a liquid to exert an upward force on an object placed in it is called buoyancy.

As more and more volume of the object is immersed in a liquid, the upward buoyant force acting on it increases. But once the object is completely immersed in a liquid, then lowering it further in the liquid does not increase the buoyant force. This means that maximum upward buoyant force acts on an object when it is completely immersed in the liquid.

Factors affecting buoyant force

1. The buoyant force exerted by a liquid depends on the volume of the solid object immersed in the liquid. As the volume of the solid object immersed inside the liquid increases, the upward buoyant force also increases. And when the object is completely immersed in the liquid, the buoyant force becomes maximum and remains constant.

The magnitude of buoyant force acting on a solid object does not depend on the nature of the solid object, e.g. if two balls made of different metals having different weights but equal volumes are fully immersed in a liquid, they will experience an equal loss in weight and thus equal upward buoyant force. This is because both the balls displace equal weight of the liquid due to their equal volumes.

1. The buoyant force exerted by a liquid depends on the density of the liquid in which the object is immersed. The liquid having higher density exerts more upward buoyant force on an object than another liquid having lower density. Thus, as the density of liquid increases, the buoyant force exerted by it also increases,

e.g. sea water has higher density than fresh water, therefore, sea-water will exert more buoyant force on an object immersed in it than the fresh water. It is easier to swim in sea water because it exerts a greater buoyant force on the swimmer.

Similarly, mercury is a liquid having very high density. So, mercury will exert a very great buoyant force on an object immersed in it. Even a very heavy material like an iron block floats in mercury because mercury exerts a very high buoyant force on iron block due to its very high density.

Why objects float or sink in a liquid A wooden block floats in water whereas a steel rod sinks in it. Thus some objects float and some sink in water.

When an object is put in a liquid, then two forces act on it:

1. Weight (W) of the object acting downwards,2. Buoyant force (B) acting upwards.An object will float or sink in a liquid will depend on the relative magnitude of these two forces acting on the object in opposite directions. Three cases arise:1. If B exerted by the liquid < W of the object, the object will sink in the liquid.2. If B = W, the object will float in the liquid.3. If B > W, the object will rise in the liquid and then float.Thus an object will float in a liquid if the upward buoyant force it receives from the liquid is great enough to overcome the downward force of its weight. For an object to float, Weight of object = Buoyant forceBut, Buoyant force = Weight of liquid displaced by the object\Weight of object = Weight of liquid displaced by the object.Thus an object will float in a liquid if the weight of object is equal to the weight of liquid displaced by it.The above relation holds true if the object has a lower density than the liquid. If the object has a higher density than the liquid, then the weight of liquid displaced will be less than the weight of object, and the object will sink.

An object will also float in a liquid if its density is equal to that of the liquid.

When we put a piece of iron in water, it sinks immediately because iron is denser than water. But a ship made from iron and steel floats on water. This is because a ship is a hollow object having a lot of air in it. Air has low density due to which the average density of ship becomes less than the density of water and the ship floats in water.

This can be explained in another way. A heavy ship floats in water as it displaces a large weight of water which provides a great buoyant force to keep it afloat.

Archimedes principleWhen an object is wholly or partially immersed in a liquid, it experiences a buoyant force (or upthrust) which is equal to the weight of liquid displaced by the object.Buoyant force acting = Weight of liquid displacedon an object by that objectArchimedes principle is applicable to objects in fluids, i.e. liquids as well as gases.

Gases (like air) exert an upward force (or buoyant force) on the objects placed in them but in most cases it is so small that we usually ignore it. It is the buoyant force due to displaced air which makes a balloon rise in air.

Buoyant force = Weight of water displaced by body.and Buoyant force = Loss in weight of body in water.\ Loss in weight of body in water = Weight of water displaced by body.Applications of Archimedes principle 1. It is used in designing ships and submarines.2. It is used in determining the relative density of a substance.3. The lactometers used for determining the purity of milk are based on Archimedes principle.4. The hydrometers used for determining the density of liquids are based on Archimedes principle.Density The density of a substance is defined as mass of the substance per unit volume.

Density = Mass of the substance/Volume of the substance

The SI unit of density is kilograms per cubic meter (Kg/m3).

The density of a substance, under specified conditions, is always the same. So, the density of a substance is one of its characteristic properties.

The density of a given substance can help us to determine its purity.

Different substances have different densities e.g. density of water is 1000 Kg/m3 which means that the mass of 1 cubic metre volume of water is 1000 kg.

Relative density The relative density of a substance is the ratio of its density to that of water.

Relative density of a substance = Density of the substance/Density of water

Since the relative density is a ratio, it has no units. It is a pure number.

The relative density of a substance expresses the heaviness (or density) of the substance in comparison to water e.g. the relative density of iron is 7.8, which means iron is 7.8 times as heavy as an equal volume of water.

The relative density of water is 1. If the relative density of a substance is more than 1, then it will be heavier than water and hence it will sink in water.

On the other hand, if the relative density of a substance is less than 1, then it will be lighter than water and hence float in water. e.g. Ice has a density of about 900 kg/m3 and water has a density 1000kg/m3.

Thus an ice cube has a relative density of 0.9 so it floats in water. The relative density of iron is7.8, so an iron nail sinks in water.

Physics Assignment-I Chapter:Gravitation

JSUNIL TUTORIAL,SAMASTIPURClass 9th(SA-II)Physics Assignment-I (For month of November)Chapter:GravitationQ1. A block weighing 1.0 kg is in the shape of a cube of length 10 cm. It is kept on a horizontal table. Find the pressure on the portion of the table where the block is kept. (ans. 1000Pa)Q2. Find the thrust acting on the human body due to atmospheric pressure. Take the surface area of a man of middle size to be 1.5m2and atmospheric pressure (1atm) =1.013105Pa.(ans.15.2 ton wt)

Q3. Calculate the mass of a body whose volume is 2 m3and density 0.52 g/cm3. (ans. 1040 kg)

Q4. A dining hall has dimensions 50m 15m 3.5m. Calculate the mass of air in the hall. Given, density of air =1.30kg/m3. (ans. 3412.5 kg)

Q5. A thread of mercury of 10.2 g is in a tube of uniform cross section 0.1cm3. Calculate the length of thread. The density of mercury is 13.6g/cm3. (ans. 7.5cm)

Q6. A cubical block of water is dipped completely in water. Each edge of the block is 1cm in length. Find the buoyant force acting on the block. (ans. 10-2N)

Q7. A body of mass 2.0 kg and density 8000 kg/m3is completely dipped in a liquid of density 800 kg/m3. Find the force of buoyancy on it. (ans. 2N)

Q8. A piece of iron of density 7.8 103kg/m3and volume 100 cm3is totally immersed in water. Calculate (a) the weight of the iron piece in air (b) the upthrust and (c) apparent weight in water. (ans. (a) 7.8N (b) 1N (c) 6.8 N)

Q9. A solid body of mass 150g and volume 250cm3is put in water. Will the body float or sink.

Q10. A solid of density 5000kg/m3weights 0.5 kg in air. It is completely immersed in water of density 1000kg/m3.(a)Calculate the apparent weight of solid in water.(ans. 0.4 kg)(b)What will be its apparent weight if water is replaced by a liquid of density 8000kg/m3? (ans. 0)

Q11. The mass of a block made of certain material is 13.5 kg and its volume is 15 10-3m3. Will the block float or sink in water. Give reason for your answer.

Q12. (a) What is the density of air in NTP? (b)What is the unit of relative density?

Q13. (a) When does a body sinks in a fluid? (b)Why does a balloon filled with hydrogen gas rise up against gravity?Q14. (a) Which has greater density: 1 kg of iron or 2 kg of iron?(b)If a hollow sphere and a solid sphere are both made of the same amount of iron, which sphere has greater average density?

Q15. (a). A body weighs 10 N in air and 8 N when fully immersed in water. How much is the buoyant force acting on the body?(a) Why are the buoys making the channel in a river are hollow spheres?

Q16. State one important effect produced by the buoyant force exerted by water.

Q17. Where does a solid weigh more- in air or in a liquid?

Q18. Name two factors on which the buoyant force depends?

Q19. What is the relationship between the buoyant force on an object and the liquid displaced by it?

Q20. The relative density of mercury is 13.6. What does this statement mean?

Q21. The density of turpentine oil is 840 kg/m3. What will be its relative density?

Q22. Explain why big boulders can be moved easily by floods.

Q23. Why is a slight blow on a cork of bottle fully filled with a liquid sufficient to break the bottle?

Q24. Why is it easier to walk on soft sand with a flat shoe than a pencil-heeled shoe?

Q25. Lead has greater density than iron and both are denser than water. Is the buoyant force on a lead pencil greater than, less than or equal to the buoyant force on an iron object of same volume?

Q26. Why do you feel lighter when you swim?

Q27. Why is a bucket of water lighter when in water than when it is taken out of water?

Q28. Why it is easier to swim in sea water tan in river water?

Q29. Two different objects are completely immersed in water and undergo same loss in weight. Is it necessary that the weight of these objects in air be also the same?

Q30. If two equal weights of unequal volumes are balanced in air, what will happen when these are completely dipped in water?Class 9th (Physics Notes on Gravitation

IX CBSE Physics Chapter : Newton : Gravity :Kepler : Orestred: Free Fall1)Gravitation:Gravitation is the force of attraction between two objects in the universe.

i) Gravitation may be the attraction of objects by the earth.Eg :- If a body is dropped from a certain height, it falls downwards due to earths gravity.

If a body is thrown upwards, it reaches a certain height and then falls downwards due to the earths gravity.

ii) Gravitation may be the attraction between objects in outer space.Eg :-Attraction between the earth and moon.

Attraction between the sun and planets.

Centripetal force:When a body moves in a circular path, it changes its direction at every point. The force which keeps the body in the circular path acts towards the centre of the circle. This force is called centripetal force.

If there is no centripetal force, the body will move in a straight line tangent to the circular path.

2)Universal law of gravitation:-The universal law of gravitation states that, Every object in the universe attracts every other object with a force which is directly proportional to product of the masses and inversely proportional to the square of the distance between them.

Let two objectsAandBof massesMandmlie at a distancedfrom each other. LetFbe the force of attraction between them.

According to the universal law of gravitation the force between the objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them

FM x m

and F1/d2

Combining the two equations

FMxm/d2

Or F = GM x m/d2whereGis a constant of proportionality calleduniversal gravitation constant

Cross multiplying we get

Fxd2=G M x morG =Fxd2/M x m

The SI unit ofGis N m2kg-2and its value is6.673 x 10-11N m2kg-23)Free fall:-The earth attracts objects towards it due to gravitational force. When an object falls towards the earth due to the earths gravitational force it is called free fall.

When an object falls towards the earth there is a change in its acceleration due to the gravitational force of the earth. So this acceleration is called acceleration due to gravity.

The acceleration due to gravity is denoted byg.The unit ofgis same as the unit of accelerationms-2From the second law of motion, force is the product of mass and acceleration.

F = ma

For free fall, force is the product of mass and acceleration due to gravity.

F = mg

mg = GM x m/d2 g = G m/d2

where Mis the mass of the earth and d is the distance between the object and the earth.

For objects near or on the surface of the earthdis equal to the radius of the earthR

mg = G M x m/ R2org =G M/ R2The value ofg is9.8 ms-24 a)Mass:-The mass of a body is the measure of its inertia. If the mass of a body is more its inertia is more.The mass of a body is constant and does not change from place to place.The SI unit of mass is kg.

b)Weight :-The weight of a body is the force with which the earth attracts the body.The force with which a body is attracted by the earth depends on its massmand acceleration due to gravityg. F = m x gSince weight of a body is the force with which the earth attracts the body,

W = m x gSincegat a place is constant ,WmThe weight of a body changes from place to place.

The SI unit of weight is the same as force Newton (N).

c)Weight of an object on the moon:The weight of an object on the earth is the force with which the earth attracts the object and the weight of an object on the moon is the force with which the moon attracts the object.

The mass of the moon is less than the mass of the earth. So the moon exerts lesser force on the objects than the earth.

The weight of an object on the moon is one sixth (1/6th) of its weight on the earth.

(5)Thrust and pressure:-a)Thrust:Thrust is the force acting on an object perpendicular to the surface.Eg :- When you stand on loose sand the force (weight) of your body is acting on an area equal to the area of your feet. When you lie down, the same force acts on an area equal to the contact area of the whole body. In both cases the force acting on the sand (thrust) is the same.

b)PressurePressure is the force acting on unit area of a surface.

Pressure =Thrust/ Area

Eg :- The effect of thrust on loose sand is larger while standing than while lying down.

The SI unit of thrust is N/m2orN m-2. It is called Pascal (Pa).

6 (a)Pressure in fluids (Liquids and gases)Fluids exert pressure on the base and walls of the container. Fluids exert pressure in all directions. Pressure exerted on fluids is transmitted equally in all directions.

(b)Buoyancy (Upthrust)When an object is immersed in a fluid it experiences an upward force called buoyant force. This property is called buoyancy or upthrust.The force of gravity pulls the object downward and the buoyant force pushes it upwards.The magnitude of the buoyant force depends upon the density of the fluid.

(c)Why objects float or sink in water?If the density of an object is less than the density of a liquid, it will float on the liquid and if the density of an object is more than the density of a liquid, it will sink in the liquid.

Activity:-Take some water in a beaker. Take a piece of cork and an iron nail of the same mass. Place them on the water. The cork floats and the nail sinks.

The cork floats because the density of cork is less than the density of water and the upthrust of water is more than the weight of the cork.

The nail sinks because the density of the iron nail is more than the density of water and the upthrust of water is less than the weight of the nail.

7)Archimedes principle:-Archimedes principle states that, When a body is partially or fully immersed in a fluid it experiences an upward force that is equal to the weight of the fluid displaced by it.

Archimedes principle has many uses. It is used in designing ships and submarines, Hydrometers used to determine the density of liquids, lactometers used to determinepurity of milk etc.

8)Density and relative density:-i)DensityThe density of a substance is the mass of a unit volume of the substance.

Density = Mass/Volume

The unit of density is kilogram per metre cube (kg m-3).

ii)Relative density:-The relative density of a substance is the ratio of the density of a substance to the density of water.

Relative density =Density of a substance/Density of water

Since relative density is a ratio of similar quantities, it has no unit.CBSE Test Papers for Class 9th(IX) Chapter Gravitation

MCQ:1 Mark Questions By Jsunil

1. Even though stone also attracts earth towards itself, earth does not move

(a) Because of greater mass of earth (b) Because of lesser mass of stone

(c) Force exerted by stone is less (d) Force exerted earth is large

2. The weight of an object is :-

(a) Greater on earth and lesser on Moon (b) Lesser on earth and Greater on earth

(c) Equal on both earth and Moon (d) None of these

3. Weight of an object has S.I, unit of :-

(a) Newton (b) kg

(c) N/Kg (d) Kg/N

4. Which of the statements is correct?

(a) Mass is constant and weight is variable (c) Both Mass and weight are variable

(b) Mass is variable and weight is constant.(d) Both Mass and weight are constant.

2Mark Questions

5. State the Universal law of Gravitation?

6. If heavier bodies are attracted more strongly by the earth, why do they not fallfaster to the ground?

7. State Archimedes Principle?

8. A stone is dropped from the edge of the roof. It passes a window 2m high is 0.1 s.How far is the roof above the window?

3Mark Questions

9. The radius of earth is 6370Km and of mars is 3400 Km. If an object weighs 200Nor earth, what will be its weight on mars. The mass of mars is 0.11 that of earth.

10. Determine the value and units of universal Gravitational constant, G?

11. What is the up thrust experienced by a cube of edge length 5cm made of ironwhen completely immersed in ethanol of density 0.8 g/cm3

12. A stone is dropped from a height of 50m on earth. At the same time, another stone is thrown vertically upwards from the ground with a velocity up wards from the ground with a velocity of 50m/s. At what height from the ground will the twostones meet (g = -10 m/s2)

9th Class - PHYSICS GRAVITATION TEST PAPER

IX-Gravitation :Important Question for SA-I

1. What The earth attracted to each other by gravitational force. Does the earth attract the moon, with a force that is greater, or smaller, or the force with which the moon attracts the earth? Why?

2. The earth attracts the moon. Does the moon attract the earth? If it does, why does the earth not move towards the moon?

3. How are ocean tides caused?

4. What do we call the gravitational force between the earth and your body?

5. The earth attracts an apple. Does the apple also attract the earth? If it does, why does the earth not move towards the apple?

6. Is the gravitational acceleration independent of mass? Name the experiment which concluded this?

7. Where do we observe the maximum value of the gravitational acceleration? Equator, poles or Mt Everest?

8. You must have seen two types of balances, one is the spring balance and the other is the one with the kabadiwalas. Which one of it would you use to measure the mass of an object? Why?

9. Why does a buffalo float on the river but not the man?

10. Why does ice float on the water?

11. Why does a ship made up of iron floats but the iron sinks?

12. How do submarines float or sink as desired?

13. Why does a mug full of water appear lighter inside the water?

14. A dead body floats in water with its head immersed in water. Explain?

15. In what direction does the buoyant force on an object, due to liquid act?

16. Why does a block of plastic piece left under water cone to the surface of water?

17. Write the condition under which the body would float on a liquid?

Class-ix-Science-physics-Gravitation Solved Questions :Numerical problems

Gravitation Solved Questions :Numerical problems

1. How does the force of gravitation between two objects change when the distance between them is reduced to half?

Answer: when the distance between the objects is reduced to half the gravitational force increases by four times the original force.

2.The gravitational force acts on all objects in proportion to their masses. Why, then, a heavy object does not fall faster than a light object?

Answer:Acceleration due to gravity does not depend on mass of object . Hence, all bodies fall with the same acceleration provided there is no air or other resistance

3.The earth and the moon are attracted to each other by gravitational force. Does the earth attract the moon with a force that is greater or smaller or the same as the force with which the moon attracts the earth? Why?

Answer:According to Newtons 3rd law of motion Every action has equal reaction in opposite direction. Since,The earth surface attracts the moon with the same force with which the moon attracts the earth and cancel them

4.If the moon attracts the earth, why does the earth not move towards the moon?

Answer:The earth is much larger than the moon so, the acceleration produced on the earth surface cannot be noticed.

5.What is the importance of Universal Law of Gravitation?

Ans: There are many importance of Universal Law of Gravitation

1. The force of attraction that binds us to the earth,

2. The motion of planets moving around the sun,

3. the motion of moon around the earth

4. The occurring of tides due to sun and moon.

6 What is Gravitation?

Answer: Gravitation is the force of attraction between two objects in the universe.

i) Gravitation may be the attraction of objects by the earth.Eg :- If a body is dropped from a certain height, it falls downwards due to earths gravity.If a body is thrown upwards, it reaches a certain height and then falls downwards due to the earths gravity.

ii) Gravitation may be the attraction between objects in outer space.Eg :- Attraction between the earth and moon.Attraction between the sun and planets

7. What is Centripetal force?

Answer: When a body moves in a circular path, it changes its direction at every point. The force which keeps the body in the circular path acts towards the centre of the circle. This force is called centripetal force.If there is no centripetal force, the body will move in a straight line tangent to the circular path.

8. State Universal law of gravitation?

Answer: The universal law of gravitation states that, Every object in the universe attracts every other object with a force which is directly proportional to product of the masses and inversely proportional to the square of the distance between them.

9.In what direction does the buoyant force on an object immersed in a liquid act?

Ans: The buoyant force acts on an object in the vertically upward direction through the center of gravity of the displaced liquid.

10.A stone is released from the top of a tower of height 19.6 m. calculate its final velocity just before touching the ground.

Ans: Given that, u = 0, g = 9.8 ms2, s = 19.6 m

Now, v2- u2= 2gs

or, v2- 0 = 2 x 9.8 x 19.6 = (19.6)2

or, v = 19.6 ms1( v is +ve due to downward direction)

IX CBSE Physics Numerical For Chapter:Gravitation

IX CBSE Physics Numerical For Chapter: Gravitation .Olympiad Practice

1. Calculate the gravitational force between a 10-kg ball and a 20-kg ball placed at a separation of 5 m.

2. Three balls A, B and C are kept in a straight line. The separation between A and C is 1 m, and B is placed at the midpoint between them. The masses of A, B, C are 100 g, 200 g and 300 g respectively. Find the net gravitational force on (a) A, (b) B, and (c) C.

3. A particle of mass m1 is kept at x = 0 and another of mass m2 at x = d. When a third particle is kept at x = d/4, it experiences no net gravitational force due to the two particles. Find m2/m1.

4. The acceleration due to gravity near the earth's surface is 9.8 m/s2, and the earth's radius is 6,400 km. From this data calculate the mass of the earth. Use any universal constant if required.

5. Two particles of mass 200 g each are placed at a separation of 10 cm. Assume that the only forces acting on them are due to their gravitational attraction. Find the acceleration of each when they are allowed to move.

6. A particle weighs 120 N on the surface of the earth. At what height above the earth's surface will its weight be 30 N? Radius of the earth = 6,400 km.

7. Suppose the earth shrinks such that its radius decreases to half the present value. What will be the acceleration due to gravity on the surface of the earth?

8. A body weighs 120 N on the earth. Find its approximate weight on the moon.

9. Calculate the value of the acceleration due to gravity at a place 3,200 km above the surface of the earth.

10. The acceleration due to gravity at a place is 0.2 m/s 2. Find its height above the earth's surface.

11. As one moves to a place 3,200 km above the earth's surface, the acceleration due to gravity reduces to 4/9 of its value at the earth's surface. Calculate the radius of the earth from this data.

12. A ball is dropped from a cliff. Find (a) its speed 2 s after it is dropped, (b) its speed when it has fallen through 78.4 m, and (c) the time taken in falling through 78.4 m.

13. A ball is thrown upwards with a speed of 39.2 m/s. Calculate (a) the maximum height it reaches, and (b) the time taken in reaching the maximum height.

14. A ball thrown upwards takes 4 s to reach the maximum height. Find (a) the initial speed with which it was thrown, and (b) the maximum height reached.

15. An object thrown upwards reaches the highest point in 5.0 s. Find the velocity with which it was thrown.

16. A stone thrown upwards attains a maximum height of 19.6 m. Find the velocity with which it was thrown.

17. A body is thrown upwards with a velocity of 20 m/s. How much time will it take to return to its original position?

18. A ball is dropped from a height 2.50 m above the floor, (a) Find the speed v with which it reaches the floor, (b) The ball now rebounds. The speed of the ball is decreased to 3u/4 due to this collision. How high will the ball rise?

19. A stone is dropped from a cliff at 2:30:30 p.m. (hour: minute:second). Another stone is dropped from the same point at 2:30:31 p.m. Find the separation between the stones at (a) 2:30:31 p.m., (b) 2:30:35 p.m.

20. A ball is thrown upwards from the surface of the moon with a velocity of 19.6 m/s. (a) How much time will it take to attain the maximum height? (b) How high will it go?

21. A flowerpot drops from the edge of the roof of a multistoried building. Calculate the time taken by the pot to cross a particular distance AB of height 2.9 m, the upper point A being 19.6 m below the roof.

22. A wicket keeping glove is dropped from a height of 40 m and simultaneously a ball is thrown upwards from the ground with a speed of 40 m/s. When and where do they meet?

23. A boy on a 78.4-m-high cliff drops a stone. One second later, he throws another stone downwards with some speed. The two stones reach the ground simultaneously. Find the speed with which the second stone was thrown.

Answers

1. 5.34 x 10"10 N 2. (a) 7.34 x1012N towards C

(b) 1.07 x1012Ntowards C (c) 1.80 x1012Ntowards A

3. 94. 6.02x1024kg 5. 1.33 x 10 ~9 m/s2

6. 6,400 km7. 39.2 m/s28. 20 N

9. 4.36 m/s2 10. Re= 38,400 km 11. 6,400 km

12. (a) 19.6 m/s (b) 39.2 m/s (c) 4 s 13. (a) 78.4 m (b) 4 s

14. (a) 39.2 m/s (b) 78.4 m 15.49 m/s . 16.19.6 m/s

17.4.08 s18. (a) 7 m/s (b) 1.4 m 19. (a) 4.9 m (b) 44.1 m

20. (a) 12 s (b) 117.6 m21. 1/7s 22. 1 s after the glove is dropped,

23. 1 m above the ground 24. 11.43

CBSE : Physics: Gravitation Notes class 9th (IX)

IX Gravitation Extra scoring notes

Gravitation is a natural phenomenon by which objects with mass attract one another.In everyday life, gravitation is most commonly thought of as the agency which lends weight to objects with mass.

It is responsible

for keeping the Earth and the other planets in their orbits around the Sun;for keeping the Moon in its orbit around the Earth,for the formation of tides;for convection (by which fluid flow occurs under the influence of a temperature gradient and gravity)for heating the interiors of forming stars and planets to very high temperatures; andfor various other phenomena that we observe.

Modern physics describes Gravitation as a consequence of the curvature of space time which governs the motion of inertial objects.Kepler's LawsJohannes Kepler, working with data painstakingly collected by Tycho Brahe without the aid of a telescope, developed three laws which described the motion of the planets across the sky.

1.TheLaw of Orbits:All planets move in elliptical orbits, with the sun at one focus.

2.TheLaw of Areas:A line that connects a planet to the sun sweeps out equal areas in equal times.

3.The Law of Periods:The square of the period of any planet is proportional to the cube of the semi major axis of its orbit.

Kepler's laws were derived for orbits around the sun, but they apply to satellite orbits as well.

UNIVERSAL LAW OF GRAVITATION :

Every object in the universe attracts every other object witha forcewhich isproportional totheproduct of their massesandinverselyproportional tothe square of the distance between them. The force is along the line joining the centres of two objects. F= G x Mm/d2If two objects A and B of masses M and m lie at a distance d from each other.Let the force of attraction between two objects be F.

According to the universal law of gravitation,

(a)The force between two objects is directly proportional to the product of their masses. That is, FM x mAnd the force between two objects is inversely proportional to the square of the distance between them, that is, F1/d2Combining the Eqs. we get F= G x Mm/d2Where G is the constant of proportionality and is called the universal gravitation constant.By multiplying crosswise, Eq. gives F d2= G M m G = (F d2 )MmThe SI unit of G can be obtained by substituting the units of force, distance and mass in Eq. as N m2kg2.The value of G was found out by Henry Cavendish (1731 1810) by using a sensitive balance. The accepted value of G is 6.673 1011N m2kg2.

IMPORTANCE OF THE UNIVERSAL LAW OF GRAVITATION

The universal law of gravitation successfully explained several phenomena which were believed to be unconnected:(i) the force that binds us to the earth;(ii) the motion of the moon around the earth;(iii) the motion of planets around the Sun; and(iv) the tides due to the moon and the Sun.TO CALCULATE THE VALUE OF gTo calculate the value of g, we should put the values of G, M and R in Eq. namely,universal gravitational constant, G = 6.7 1011N m2kg-2,mass of the earth, M = 6 1024kg, andradius of the earth, R = 6.4 106m.

F = m a

F = G Mm/d2m a = G Mm/d2mg = G Mm/d2g = G M/d2g = (6.7 1011N m2kg-2x6 1024kg)/( 6.4 106m)2g9.8 m/s2Thus, the value of acceleration due to gravity of the earth,g= 9.8 ms-2

MOTION OF OBJECTS UNDER GRAVITATIONAL FORCE OF THE EARTHWe know that an object experiences acceleration during free fall due to gravitational force.

Gravitational acceleration experienced by an object is independent of its mass.

This means that all objects hollow or solid, big or small, should fall at the same rate.According to a story, Galileo dropped different objects from the top of the Leaning Tower of Pisa in Italy to prove the same.As g is constant near the earth, all the equations for the uniformly accelerated motion of objects become valid with acceleration a replaced by gThe equations are:v = u + at S= ut + at2 v2= u2+ 2asWhere u and v are the initial and final velocities and s is the distance covered in time, t.In applying these equations, we will take acceleration, a to be positive when it is in the direction of the velocity, that is, in the direction of motion. The acceleration, a will be taken as negative when it opposes the motion.Example: A car falls off a ledge and drops to the ground in 0.5 s. Let g = 10 m s2 (for simplifying the calculations).(i) What is its speed on striking the ground? (ii) What is its average speed during the 0.5 s?(iii) How high is the ledge from the ground?Solution: Time, t = second Initial velocity, u = 0 m s1Acceleration due to gravity, g = 10 m s2 Acceleration of the car, a = + 10 m s2(i) speed v = a t v = 10 m s2 0.5 s = 5 m s1(ii) average speed = (u +v )/2 = (0 m s1+ 5 m s1)/2 = 2.5 m s1(iii) distance traveled, s = a t2 = 10 m s2 (0.5 s)2 = 10 m s2 0.25 s2= 1.25 mThus,(i) Its speed on striking the ground = 5 m s1(ii) Its average speed during the 0.5 s = 2.5 m s1(iii) Height of the ledge from the ground = 1.25 m.

Example:An object is thrown vertically upwards and rises to a height of 10 m. Calculate (i) the velocity with which the object was thrown upwards and (ii) the time taken by the object to reach the highest point.

Solution: Distance traveled, s = 10 mFinal velocity, v = 0 m s1Acceleration due to gravity, g = 9.8 m s2Acceleration of the object, a = 9.8 m s2(i) v2= u2+ 2a s0 = u2+ 2 (9.8 m s2) 10 mu2= 2 9.8 10 m2s2u = 14 m s-1(ii) v = u + a t0 = 14 m s1 9.8 m s2 tt = 1.43 s.Thus,(i) Initial velocity, u = 14 m s1, and(ii) Time taken, t = 1.43 s.Mass:-mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force.Weight:-Weight is the force of gravity acting on a mass. Weight should be measured in Newtons and has a direction component (vector). This direction is normally downward due to gravity.

We know that the earth attracts every object with a certain force and this force depends on the mass (m) of the object and the acceleration due to the gravity (g).

The weight of an object is the force with which it is attracted towards the earth.We know that F = m a,that is, F = m g.The force of attraction of the earth on an object is known as the weight of the object. It is denoted by W. W = m gWEIGHT OF AN OBJECT ON THE MOON

The weight of an object on the earth is the force with which the earth attracts the object. In the same way, the weight of an object on the moon is the force with which the moon attracts that object. The mass of the moon is less than that of the earth. Due to this the moon exerts lesser force of attraction on objects.Let the mass of an object be m. Let its weight on the moon be Wm. Let the mass of the moon be Mm and its radius be Rm. By applying the universal law of gravitation, the weight of the object on the moon will beWm= G x Mm xm/R2m

Let the weight of the same object on the earth be We. The mass of the earth is M and its radius is R.From Eqs. and we have,We = G Mxm/d2Substituting the values, we getWm = 2.431 1010G x mand We=1.474 1011G mDividing Eq., we getWm/We =1/6Or, Weight of the Object on Moon/Weight of the Object on Earth = 1/6Weight of the object on the moon = (1/6) its weight on the earthExample:An object weighs 10 N when measured on the surface of the earth. What would be its weight when measured on the surface of the moon?Solution: We know, Weight of object on the moon = (1/6) its weight on the earth.That is, Wm = We/6 = 10/6=1.67 NThus, the weight of object on the surface of the moon would be 1.67 N.

Thrust and PressureThurst:Thrust is a reaction force described quantitatively by Newton's Second and Third Laws. When a system expels or accelerates mass in one direction the accelerated mass will cause a proportional but opposite force on that system.Pressure:Pressure (symbol: p or sometimes P) is the force per unit area applied to an object in a direction perpendicular to the surface. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.Pressure = Thrust/ AreaThe SI unit of pressure is N/m2or N m2.

Example:A block of wood is kept on a tabletop. The mass of wooden block is 5 kg and its dimensions are 40 cm 20 cm 10 cm. Find the pressure exerted by the wooden block on the table top if it is made to lie on the table top with its sides of dimensions (a) 20 cm 10 cm and (b) 40 cm 20 cm.

Solution: The mass of the wooden block = 5 kg The dimensions = 40 cm 20 cm 10 cmHere, the weight of the wooden block applies a thrust on the table top.That is, Thrust = F = m g = 5 kg 9.8 m s2 = 49 NArea of a side = length breadth = 20 cm 10 cm = 200 cm2= 0.02 m2 From Eq. Pressure = 49/0.02 m2= 2450 Nm-2When the block lies on its side of dimensions 40 cm 20 cm, it exerts the same thrust.Area= length breadth = 40 cm 20 cm= 800 cm2= 0.08 m2Or, Pressure = 49/0.08 m2= 612.5 Nm-2The pressure exerted by the side 20 cm 10 cm is 2450 N m2and by the side 40 cm 20 cm is 612.5 N m2.PRESSURE IN FLUIDSAll liquids and gases are fluids. A solid exerts pressure on a surface due to its weight. Similarly, fluids have weight, and they also exert pressure on the base and walls of the container in which they are enclosed. Pressure exerted in any confined mass of fluid is transmitted undiminished in all directions.WHY OBJECTS FLOAT OR SINK WHEN PLACED ON THE SURFACE OF WATER?The nail sinks. The force due to the gravitational attraction of the earth on the iron nail pulls it downwards.There is an up thrust of water on the nail, which pushes it upwards. But the downward force acting on the nail is greater than the up thrust of water on the nail. So it sinks.The cork floats while the nail sinks. This happens because of the difference in their densities.

The density of a substanceis defined as the mass per unit volume. The density of cork is less than the density of water. This means that the up thrust of water on the cork is greater than the weight of the cork. So it floats.The density of an iron nail is more than the density of water. This means that the up thrust of water on the iron nail is less than the weight of the nail. So it sinks.Therefore, objects of density less than that of a liquid float on the liquid. The objects of density greater than that of a liquid sink in the liquid.Archimedes Principle Archimedes' principle, states that a body immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid.

The principle applies to both floating and submerged bodies and to all fluids, i.e., liquids and gases.

It explains not only the buoyancy of ships and other vessels in water but also the rise of a balloon in the air and the apparent loss of weight of objects underwater.In determining whether a given body will float in a given fluid, both weight and volume must be considered; that is, the relative density,orweight per unit of volume, of the body compared to the fluid determines the buoyant force. If the body is less dense than the fluid, it will float or, in the case of a balloon, it will rise. If the body is denser than the fluid, it will sink.

Relative density also determines the proportion of a floating body that will be submerged in a fluid. If the body is two thirds as dense as the fluid, then two thirds of its volume will be submerged, displacing in the process a volume of fluid whose weight is equal to the entire weight of the body. In the case of a submerged body, the apparent weight of the body is equal to its weight in air less the weight of an equal volume of fluid.

Relative Density = Density of substance / Density of water

Example: Relative density of silver is 10.8. The density of water is 103 kg m3. What is the density of silver in SI unit?Solution:Relative density of silver = 10.8Relative density = Density of Silver/Density of WaterOr, Density of silver = Relative density of silver density of water= 10.8 103 kg m3.CBSE Practice Papers Class IX Gravitation

CBSE SA-II Physics Chapter-Gravitation (Newtons laws for Gravitation)

1. Sate Newton's law of motion. Derive it.

2. Define

a) Gravity and an expression for acceleration due to gravity

b) Pressure

c) Free fall

3. If the earth attracts an apple does the apple also attract the earth? If yes, why does the earth not move towards the apple?

4. Why does a mug full of water feel lighter inside water?

5. A perpendicular force of 50N acting on a surface generate a pressur of 250pa. Calculate area of cross section of surface on which pressure is acting.

6. Why and when does acceleration due t gravity acting on a body change.

7. A body has 40kg mass. Calculate it's wt. when it is taken to a planet whose mass is 4 times the earth and radius half then that of the earth.

8. How does the wt. of a body gets affected when the is taken to poles from equator?

9. Wy does the moon not actujally fall on the surface of the earth?

10. State the difference between mass and weight.

11. A bar of gold has mass of 100g ad weight is9.8 N at some place when it is taken to some place at equator mass remains 100g but wt. is