## Gravitation

Gravity is an attracting force, Gravitational force is always attractive in nature and is one of the weakest force. In this chapter,we will be studying about the gravitational force in detail.

### Newton's universal law of gravitation.

• Do you know that every object in the universe attracts other object!!! and when there is a attraction there must be a force which is being used to help objects attract each other.
• According to Newton's law of gravitation, every object in the universe attracts every other object with a force which is directly proportionate to the product of the masses of the objects and inversely proportionate to the square of the distance between the centres of the 2 objects.
• By this law, we derive the following formula:-
• F=GMm/r2 (G is the universal gravitational constant and its value is the same in the whole universe, M and m are the masses and r is the distance between the centres of the 2 object)

### Do You Know ?

• Gravitational force is the weakest force in nature.
• 'G' is the Universal gravitation constant i.e. its value remains the same in the whole universe and its value is G=6.67x10-11 Nm2/kg2

### Importance of gravitational force

Gravitational force is a very important force and has many importance.
• The force of attraction that binds us to the earth.
• The motion of planets moving around the sun.
• The motion of moon around the earth.
• The occurring of tides due to sun and moon.

### Acceleration due to gravity Value of 'g'

It is the acceleration which a body experiences, when it falls towards the earth due to earth’s gravitational pull. It is denoted by 'g'. Its value is different at every place on earth. we usually take its value as 9.8 m/s2.

### Do You Know ?

• 'g' does not depend on the mass of the object.
• According to Newton’s Second law :- F= ma i.e. force = mass*acceleration
• The value of 'g' on moon is 1/6 the value of 'g' on Earth. As a result a object weighs 6 times more on earth.
• Value of `g’ is different on different planets, so weight will also be different.
• Weight of a body decreases with height and also with depth from the surface of the earth.

### Value of 'g'

According to Newton’s Second law :- F= ma and for a object falling freely towards the earth it  becomes F = mg:-
Explanation: force = mass*acceleration and when an object freely fall towards the earth it experiences acceleration of 9.8 m/s2  ='g'

Newton’s Gravitation law  F = GMm/r2
When we comparing mg=GMm/r2 (m gets cancelled on both sides) and we get g = GM/R2 (M= mass of the earth)

### Difference between ‘g’ & ‘G’

 ‘g’ ‘G’ It is the acceleration which a body experiences when it falls towards the earth due to earth’s gravitational pull. It is a universal gravitational constant. Its value is different at different points on the earth. Its value remains same everywhere, as it is a constant It is a vector quantity. It is a scalar quantity. The value of 'g' on the surface of earth is 9.8 m/s2 The value of G=6.673 x 10-11 Nm2/kg2   . Its value can be zero—at the centre of the earth or in space. Its value can never be zero.

### Variation in the value of 'g'

The value of 'g' is not constant and changes due to these factors:

• The earth is not spherical in shape but it is oval in shape due to which the value of 'g' is more at poles.
• Value of g decreases with the altitude above the surface of the earth .
• Value of g decreases as we go deep into earth.

### Do You Know ?

There are 3 equations of motion:-
• v = u + a t
• s = u t + 1/2at2
• v2 –u2 =2as

### Equations of motion for a freely falling body

The equations of motions can be applied on an object which is freely falling towards earth. These are:-
• v = u + g t
• h = u t + 1/2gt2
• v2 –u2 =2gh

Replacing 'a' by 'g' and 's' by 'h'
Some important points:-

1. For a freely falling body, u=0 at the maximum height.
2. When a body is thrown up, its v=0 at the maximum height.
3. If a body thrown up, g= - 9.8m/s2.
4. If a body thrown down, g = 9.8m/s2.

### Difference between mass & weight

 MASS WEIGHT It is the quantity of matter in an object. It is the force by which an object is attracted by the earth. Its value remains same everywhere, as it is a constant. Depends on mass & 'g'.(W=mg) It is a scalar quantity. It is a vector quantity. SI unit is kilogram. SI unit is Newton. Mass is measured by a beam balance. Weight is measured by a spring balance. Mass can never be zero. Weight can be zero at places like centre of the earth or in space where the value of 'g' is 0

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