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Gravitation Class 9 Science Chapter, Explanation, Notes, Question Answers

CBSE Class 9 Science Chapter 10 Gravitation, Explanation, Examples, Question Answers

Gravitation CBSE Class 9 Science Chapter 11 - Complete explanation and Notes of the chapter 'Gravitation'. Topics covered in the lesson are, Introduction, Newton’s law of gravitation, Gravitational constant and its units, Freely falling bodies, Acceleration due to gravity, Derivation of expression for g, Prove gm=1/6th of ge, Weight and mass, Prove Wm=1/6th of We, Thrust, Pressure, Archimede’s principle and its application, Density, Relative density, Application of pressure, Buoyant force and its causes. Given here is the complete explanation of the chapter, along with all the important questions and NCERT solutions to book questions have also been provided for the ease of students.

 

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Class 9 Science Chapter 10 - Gravitation

Part 1 Gravitation

 

 

Topics to be covered

 

Introduction

Derivation of expression for g

Newton’s law of gravitation

Prove gm=1/6th of ge

Gravitational constant and its units

Weight and mass

Freely falling bodies

Prove Wm=1/6th of We

Acceleration due to gravity

 

 

 

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Introduction

As we all know that if we release anything, it falls down towards the Earth. Suppose you are playing with a ball and it slips through your hands. Then where does it go? It doesn’t move upwards, rather, it moves downwards. This is a fact that there is something in the earth that attracts everything towards itself or we can say that earth acts as a magnet and attracts everything towards itself. Actually, the attractive force or magnet is called as gravitational force or gravity.
Gravity: It is the force with which the earth attracts all objects (smaller or bigger, heavier or lighter) towards itself.

See Video for Explanation of the Part 1 Lesson

 

 

Newton’s law of Gravitation

As we discussed that earth attracts objects, likewise, it was observed by Newton that all objects attract each other though the magnitude of attraction can be smaller, but the attractive forces do exist.
According to this law, everybody in the universe attracts every other body with a force which is directly proportional to their masses & inversely proportional to the square of the distance between them.
Mathematically, it can be stated as follows-

 

 

To convert the expression into a formula, we need to remove the proportionality sign and make use of constants. Sometimes, the constant has a specific name, value and units and sometimes it has no name, value or units. In this case, the constant has a specific name, value and units.

Gravitational constant and its units

According to the law:

The value for G is always the same at all places.
If we need to define gravitational constant, then, we have to take all values as unity except G that is:
Consider two bodies of masses 1 kg each separated by distance 1 m, then the expression becomes:
G=F x (1)2/1 x 1
So, we can define G as:
Gravitational constant is equal to the force of attraction that exists between two bodies of masses separated by distance one meter.

If we take this concept in notice that all bodies attract each other, then why do we always see all objects moving towards earth, why not movement in the earth towards the objects.
This is because as we know: 
F= m.  a
Or       
a ∞ 1/m
According to it, More is the mass, less is the acceleration produced.
So, we know that mass of earth is larger as compared to objects placed on it. Therefore,  acceleration is produced in earth but the magnitude is very small (almost nil) that we hardly see it moving.

 

Effects of force of gravitation are as follows-
a)      It holds the atmosphere in place.
b)      It keeps planets & sun, satellites in their objects.
c)      It helps in the formation of tides.
d)      It keeps water retained in oceans.

 

Freely falling bodies

Suppose a book is lying on a shelf and due to any reason, it falls down. When it falls, it moves towards gravity and at that time only gravitational force is acting on it. This type of body is called freely falling body.
The bodies that fall under the influence of gravity alone are called freely falling bodies.

 

Acceleration due to gravity

In the above example we saw that the book falls down and it is referred as freely falling body and the acceleration produced in it is only due to gravity. Thus, the acceleration is called acceleration due to gravity.

It is the acceleration produced in freely falling bodies due to the earth’s gravity.
It is denoted by ‘g’.

Derivation of expression for g

Expression for ‘g’

Consider a body on the surface of earth such that ‘m’ is mass of body & M is mass of earth & R is the distance between earth and person. If the body falls on the surface of earth then we know,

 

Hence proved.
Value of ‘g’ on earth

 

 

Please note that the value of g is different on different planets as mass and radius is different for all.

Prove g of moon =1/6th of g of earth

 

 

Please note: the value of ‘g’ decreases as we move:-

    1. From poles to equator
    2. Away from earth on hills
    3. Into the earth i.e. deep mines.

 

Weight and mass

We often use the terms mass and weight interchangeably, thinking that both are synonyms but actually there is a difference between the two. For example, if you go to the market to buy tomatoes, you ask the grocer to give you a particular weight of tomatoes or this much mass of tomatoes but actually that is wrong. That is measured in mass not weight .So, let’s find out the difference between the two terms.             

Mass is actually the quantity of matter contained in a body. It is measured in kg and the smaller unit is grams. It is a scalar quantity. It can never be zero as everything has certain mass. Moreover, mass remains the same at all places, it doesn’t change with a change in the place or planet.

 

Weight: It is the pull exerted on a body by earth or a force with which the earth attracts objects towards itself. It is a vector quantity and is measured in Newtons. Weight is different at different places as it depends upon ‘g’ and it is different at different places or planets.

So, it is given by:
W = m.g

Please note that on earth, ‘g’ is maximum at the poles and minimum at the equator. In the same way, weight is minimum at the equator and maximum at the poles and zero at the centre of the earth because in centre ‘g’ is zero.

Prove Wm = 1/6th of We

Equations of motion for freely falling bodies are as follows-

1st        V = u + gt

2nd       H = ut + 1 gt2
2

3rd        V2 = u2 + 2gh 

Please Note-

  1. 'g', is +ve when body falls towards earth.-ve when body moves upward.
  2. 'g', is –ve when body moves upward.
  3. When the body is dropped from a height, Initial velocity (u) = 0
  4. When the body is thrown upwards, then final velocity (v) = 0

 

Part 2 - Thrust & Pressure

 

Topics to be covered:

 

Introduction

Archimede’s priciple and its application

Thrust

Density

Pressure

Relative density

Application of pressure

NCERT Book solutions

Buoyant force and its causes

 

 

See Video for Explanation of the Part 2 Lesson

 

 

Introduction

You must have seen the carpenter embedding a nail in a wooden board. When he does, he applies force on the hammer which further applies force on the nail placed perpendicular on the wooden board. As a result, it sinks into the wooden board. This force that the hammer applies is a perpendicular force on the nail which is called thrust. This  force is similar to the force that we exert to open a box or to push a door but the only difference is that the direction here is perpendicular.

 

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Thrust

It is the perpendicular force acting on a body. Its unit is the same as that of force that is Newton and is denoted by the same symbol, ‘F’.
Let us do one more activity in which we try to push our thumb on a board and on the other hand, we try to push a pointed pin into the board. In both the cases, thrust is acting. What do you observe? Which out of two gets embedded in the board? Obviously, the drawing pin and not the thumb gets embedded, because the pin’s end is pointed. The logic behind it is that when the pin is pointed, it means that lesser area is in contact with the board due to which the force that is acting on the board is not spreading. Moreover, the force acting per unit area is large, that is the reason that the thumb, due to a large area of contact does not get embedded.

Pressure

On the basis of the above activity, we can say that force acts per unit area whether it is of a large magnitude or a smaller magnitude. This force acting on given area that lets the pin get embedded into the board is known as pressure.
Pressure: It is the force per unit area acting on an object.
Pressure = Force / Area
Unit: Pascal (Pa)
To define 1 Pascal, we take area and force as unity that is:
P=F/A
Or, 1Pa=1N/1m2
Therefore, pressure is said to be 1 Pascal, when force of 1 Newton acts on 1m² area.
We have seen that there are certain factors on which pressure depends that is:

  1. Force
  2. Area

 

Force: more is the magnitude of force, more is the pressure exerted.
For example: If we push the pin harder, it will exert more pressure and it will move into the wooden board more easily..
Area: less is the area, more is the pressure.
For example: If we push the thumb in the board, it doesn’t gets embedded because the area in contact is more, due to the reason the magnitude of pressure becomes low.
Please note: the same force can produce different pressures depending upon the area over which it acts. Like, if the force acts on a large area of object, it produces a small pressure but if the same force acts over a small area, it produces a large pressure.
We can also define pressure as: Thrust per unit area because in case of pressure, the force acts always perpendicularly.

Application of pressure

Explanation of everyday observations
You must have noticed that the School bags with wide strap are easy to carry as compared to narrow strap bags. The reason is given below:
We know that pressure is inversely proportional to area. So, more is the area, less is the pressure. Straps are wide because by keeping them wide, the area increases. Due to this, the pressure exerted on the shoulders becomes less and a child can easily lift the bag on his shoulders.
We have seen that it is easier to peel vegetables with a sharp knife than a blunt knife. The reason being:
We know that pressure is inversely proportional to area. That is more is the area, less is the pressure or vice-versa. A sharp knife has less area so; pressure exerted by it is more. Hence, vegetables can be easily peeled off.
Likewise, it is difficult to move with pencil heels on sand - We know that pressure is inversely proportional to area.
Pencil heels have very less area which is in contact with sand. So, the pressure exerted is quite high. As a result, the heels get sunk into the sand.
Similarly we observe:
Tractors have broad tyres so that they can exert less pressure.
Tip of needle is sharp
Rear tyres of heavy vehicles are double so as to exert less pressure and move smoothly.

Pressure in Fluids
We know there are three states of matter, that is, solids, liquids and gases. Out of the three, liquids and gases possess the property to flow therefore, they are referred to as fluids.

 

Fluids: The substances that can flow are called fluids. For example: Liquids and gases. Water and air are common examples of fluids.
For example: you all enjoy the festival of colors that is Holi, when we play with colours and water balloons, in order to fill those balloons, we make use of pichkari, from which the water comes out and exerts pressure on balloon due to which it gets filled.
So, as solids exert pressure on a surface due to their weight, likewise, the fluids also exert pressure as they too have weight. Like, if we keep the fluid in a container, then it exerts pressure on the walls (inner) of the container, in all directions.

Buoyant Force and it’s causes

Suppose we try to push the mug towards bottom into a bucket of water. Then what do we notice when we release it. We notice that when we release it, it doesn’t remain at the bottom, it is pushed by water in upward direction. That means that water exerts force on it and that is always in the upward direction. This is called buoyant force.
Buoyant force: The upward force acting on a body, when it is partially or fully immersed in any liquid. This is also called Buoyancy.

Cause of Buoyancy

When an object is immersed fully or partially in a fluid, then force acts on it from all four sides. The side forces being equal and opposite, cancel each other’s effect. The forces acting from up and down are not equal. The force exerted from downward is more. Therefore, it experiences a net upward force.
Factors on which Buoyant Force depend are as follows-
1.      Volume of object immersed in fluid
2.      Density of liquid

Dependence on volume of object immersed: As the volume of object immersed inside the liquid increases, the buoyant force also increases. But when the object is fully immersed, the magnitude of this force becomes maximum and constant.

 

For example, if we have two balls made up of different metals having different weights but equal volumes are fully immersed in liquid, then they will experience the same upward force because equal volume of both balls is immersed.

Dependence on the density of liquid: More is the density of liquid, more will be the upward force exerted by liquid.

That is the reason it is easier to swim in sea water because seawater due to high density exerts greater buoyant force to the swimmer whereas in case of fresh water the buoyant force is not that large.

Archimede’s principle and its application

 

As we noticed, the mug immersed in water bucket comes up when released but sometimes it comes with more pressure and sometimes it comes with less pressure. We observe that the buyont force is different. Let’s see what is the reason behind it.
We see that when an object is partially or fully immersed in liquid, the upward force acts on it which is equal to volume or weight of liquid displaced by it.
Upthrust acting on an object = Weight of liquid displaced by the object
Buoyant Force = Volume of liquid displaced.

Applications of Archimedes’ Principle are as follows-

  1. It is used in determining relative density of substance.
  2. Hydrometers are used to measure density of liquids.
  3. Lactometers are used for determining purity of milk.
  4. Archimedes’ principle is used for designing ships and submarines.

 

Floatation

Have you seen that when we drop a certain thing in fluid like water then some objects float & some sink. Like, when we drop plastic cup in water, it floats, but the stone dropped in it sinks.

The reason is that when the object is placed in water, two forces acts on it:

  1. Weight of object acting downwards.
  2. Upthrust acting upwards.

 

Now, whether the object floats or sinks, that depends on which force is greater out of the two forces mentioned above.

 

Please note:
If upthrust is more, the object floats.
If weight is more then the object sinks.
If both are equal, then the object floats in the liquid not on the surface.

Do you know how boats float in water: When a boat is lowered into the water, it displaces more and more water due to which upthrust increases. The boat stops sinking into water when buoyant force acting is just enough to support the weight of the boat. When the boat is floating, the weight of fluid displaced by the submerged part of the ship is equal to the weight of boat.

 

Density

Every substance is a part of matter, but how matter is present in unit volume that gives rise to another physical quantity that is density.
Density: It is defined as mass per unit volume of body.
Formula : Density = Mass/volume
Unit = kg/ m³

 

Relative Density

If we compare the density of substance with density of water that it is referred to as relative density. It is the ratio of density of a substance to the density of water.
It has no units.
The relative density actually expresses the heaviness of substance in comparison to that of water.
The relative density of iron is 7.8. It means that iron is 7.8 times heavier than water.

NCERT book solutions

1. State universal law of gravitation?
Ans: According to this law: Everybody in the universe attracts every other body with a force which is directly proportional to their masses & inversely proportional to square of distance between them.

2. Write the formula to find the magnitude of force between the object and the earth lying on earth surface?
Ans:

 

3. What do you mean by free fall?
Ans: When the body falls under the influence of gravity alone, it is called free fall.

4. What do you mean by acceleration due to gravity?
Ans: The acceleration produced in freely falling bodies is called acceleration due to gravity.

5. Why the weight of an object on the moon is 1/6th of that on earth?
Ans :

 

6. How does the force of gravitation changes between the objects when the distance between them is halved?
Ans: When the d is halved, F becomes four times.
7. Gravitational force acts on all objects in proportion to their masses. Why then a heavy object does not fall faster than a light object?
Ans: Bodies fall faster or later, that depends upon acceleration due to gravity not the masses.

8. What is the magnitude of the gravitational force between the earth and 1 kg object on its surface?
Ans:

 

9. Difference between mass & Weight?
Ans:

Mass

Weight

1. It is the quantity of matter contained in a body

1. It is the force with which the Earth attracts an object towards itself.

2. It can never be zero

2. It can be zero

3. It remains same at all places.

3. It changes from place to place

4. Unit is kg

4. Unit is Newton

5. Scalar quantity

5. Vector quantity

 

10. If the moon attracts the earth, why does the earth do not move towards the moon?
Ans: The earth does not move towards the moon because of centripetal force.

11. What happens to the force between two objects ,if
(i) The mass of one object is doubled?
(ii) Distance between them is doubled?
(iii) mass of both doubled?
Ans:
(i) when mass is doubled, F is also doubled.
(ii) When d is doubled, F becomes 1/4th
(iii) When both masses are doubled, F becomes 4 times.

12. What is the importance of the universal law of gravitation?
Ans: The importance of the universal law of gravitation is as follows-

  1. It holds the atmosphere in place
  2. It keeps planets & sun, satellites in their objects.
  3. It helps in the formation of tides.
  4. It keeps water in oceans.

 

13. What is the acceleration of free fall?
Ans: Its average value on earth is 9.8m/sec2 .

14. What do we call the gravitational force between earth and object?
Ans: It is simply called as gravity .

15.Gravitational force on the surface of the moon is 1/6th strong as gravitational force on earth .what is the weight in Newton of a 10kg object on the moon and on the earth ?find the mass of each ?
Ans:

 

16. A ball is thrown vertically upwards with the velocity of 49m/sec. calculate the maximum height to which it reach and total time taken by it to return to the surface of earth ?
Ans.

 

17. A stone is released from the top of tower of height 19.6m.Calculate the final velocity .Take g=9.8m/sec2?
Ans.

 

18. a stone is thrown vertically  upwards with the velocity 40m/sec.Find the maximum height reached by the stone .what is the displacement and total distance covered by stone ?
Ans.

 

19. Calculate force of gravitation between the earth and the sun, given the mass of sun=2 x 1030Kg.The average distance between two 1.5 x 1011m?
Ans.


20. A stone is allowed to fall from the top of tower 100m high and at the same time another stone is projected up from ground with velocity 25m/sec .Find when and where will they meet ?
Ans: let the two meet after 4 sec at C,a distance x below top of two.

 

 

21. What do you mean by buoyancy?
Ans: Buoyancy is the upward force acting on an object when it is partially or wholly immersed in a fluid.

22. Why does an object float or sink when placed on the surface of water?
Ans: If the density of an object is more than water, it will sink in water. If the density of an object is less than water, it floats.

23. You have a bag of cotton and an iron bar each indicating a mass of 100kg when measured on a weighing machine. In reality, one is heavier than the other. Can you say which one is heavier and why?
Ans: Cotton is heavier than iron since its decrease in weight due to air displaced is more than the weight of air displaced by iron.

24. Why does a block of plastic released under water come to the surface of water?
Ans: The density of plastic is less than that of water. When plastic block is dipped completely in water, the weight of water displaced is more than the weight of the block. The block will dip to such an extent that the weight of water displaced is equal to the weight of the block.

25. In what direction does the buoyant force of an object immersed in liquid acts?
Ans:  The buoyant force of an object immersed in liquid acts in upward direction.

26. The volume of 50g of a substance is 20cm3. If density of water is 1gcm-3, will the substance float or sink?
Ans: Density =mass/volume =50/20=2.5gcm-3

27. The volume of 500g sealed packet is 350cm3. Will the packet float or sink in water if the density of water is 1gcm-3? What will be the mass of water displaced by the packet?
Ans: Density of packet =mass/volume
500/350=1.43gcm-3

28. Since density of packet is more than water, it will sink in water. The water displaced due to complete sinking is equal to volume of packet that is 350cm3?
Ans: Mass of water displaced =volume x density of water
=350 x 1
=350g

 

 

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