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GRAVITATION
How Gravitation Came
 It is said that once the great English scientist Isaac Newton was sitting in his garden under an apple tree when an apple from the tree fell on him.
 Newton said that an apple falls down from the tree towards the earth because the earth exerts a ‘force of attraction’ on the apple in the downward direction.
This force of attraction exerted by the earth is called its gravity.
 Similarly, a leaf falls down from a tree due to the gravity of the earth.
 In fact, the earth attracts (or pulls) all the objects towards its center.
What is Gravitation
The force with which the earth pulls the objects towards it is called the gravitational force of earth or gravity (of the earth).
How Gravitation Works in Daily Life
 It is due to the gravitational force of the earth that all the objects fall towards the earth when released from a height.
 The gravitational force of earth (or gravity of earth) is responsible for holding the atmosphere above the earth; for the rain falling to the earth; and for the flow of water in the rivers.
 It is also the gravitational force of earth (or gravity of earth) which keeps us firmly on the ground (and we do not float here and there).
 Similarly, a ball is thrown upwards also falls back to the earth due to the gravitational force of the earth.
 Since the gravitational force of earth (or gravity of earth) pulls the objects in the downward direction, therefore, a force has to be applied by us to raise an object to a height above the surface of the earth (to overcome the gravitational force of earth).
NEWTON’S LAW OF GRAVITATION
 The questions like why did the apple fall on the ground and why didn’t the satellite fall on the ground fascinated Newton.
 He came up with the universal law of gravitation.
”Everybody in the universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them ”.
 That is if objects are very close to each other than the distance between them is less and so the force with which they attract each other will be more.
Suppose you have a ball and a box both lying on the floor. Do they actually start moving towards each other?

 According to the universal law, the ball and the box should be moving towards each other.
 But in actual this does not happen.
 This is because the force with which they are attracting each other is very much small.
 So here if the mass of the ball is m_{1 }and the mass of the box is m_{2} then, F ∝ m_{1 }m_{2, }and is inversely proportional to the distance between them.
 F ∝ 1/r²
 As you move the objects far away from each other the force will be less and if the objects are brought close then the force will be much greater.

The Mathematical Form of Law of Gravitation
 We have two masses m_{1 }and m_{2}
 We know that, F ∝ m_{1 }m_{2 }and F ∝ 1/r²
 From these two we can say that, F ∝ m1m2/r²
 Now we need to convert this proportionality into equality, So we introduce a gravitational constant,
 F = Gm1m2/r²
 G = Gravitational constant.
 SI unit of G is Nm² kg²
 The value of G is 6.673×10^{11 }Nm² kg²
Suppose you have kept two pens on the table and you want to know the force of attraction between them, you can find out easily if you know the masses of the two pens, we can calculate the force by the above universal formula.
Value of gravitational constant G
The gravitational value G numerically equal to the force of gravitation which exists between two bodies of unit mass kept at a unit distance from each other.
This value is extremely small . It states that the force of gravitation between two ordinary bodies is very weak.
The force of gravitation is a vector quantity and it acts along the line joining centers of mass of two bodies.
Importance of Newton’s Universal Law of Gravitation
 It has explained to us the force that binds us to the earth i.e how every object is pulled from the earth.
 It explains the motion of the moon around the earth.
 Also, the motion of the planets around the earth is explained.
Summary of What We Learnt in this Topic Gravitation
 This force is attracting the apple towards the earth. in other words, the force which is acting between the ground/earth and the apple is called gravitational force.
 According to Sir Isaac newton every objects in the universe attracts every other objects with a certain force.
 the force with which two objects attract each other is called gravitational force.
 If the masses of the objects is very small,then the gravitational force acting between them is very small and cant be detected easily.
 For example when two stones lying on the ground also attract each other but since their mass is small hence we don’t see the stone moving towards each other.
 Always do note that the gravitational force or the force of gravity is an attractive force.