## Unit – I A |

## Newton’s Law of Gravitation:

### Statement:

- Every particle of matter in the universe attracts every other particle of matter with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
#### Explanation :

Where ‘m_{1}’ and ‘m_{2}’ are point masses and r is the distance between the particles.

- Where ‘G’ is constant of proportionality and known as Universal gravitation constant. The value of ‘G’ in S.I. System is is 6.673 10
^{-11}N m^{2}kg^{-2}. The value of ‘G’ in c.g.s. System is 6.673 10^{-8}dyne cm^{2}g^{-2}. Its dimensions are [M^{-1}L^{3}T^{-2}].

### Characteristics of Gravitational Force:

- The gravitational force between two bodies forms the action-reaction pair.
- The gravitational force between two masses is always that of attraction.
- The gravitational force between two masses is always acting along the line joining the centre of the two masses. Hence it is a central force.
- The gravitational force between two masses is independent of the medium between the two masses and their sizes or distribution of mass.
- The gravitational force between two bodies does not depend upon the presence or the absence of other bodies.
- If the masses of the body are small, the gravitational force between them is negligible. If the masses are large like that of the sun and the earth, the gravitational force of attraction is considerable.
- Gravitational force is a conservative force because the work done by the gravitational force is independent of the path between initial and final position.
- Mathematical expression for Newton’s law of gravitation is sometimes written as

- The negative sign indicates the force of attraction.

### S.I. Unit of G:

- By Newton’s law of gravitation the gravitational force between two point masses ‘m
_{1}’ and ‘m_{2}’ separated by distance ‘r; is given by

- The SI unit of constant of gravitation is N m
^{2}kg^{-2}and c.g.s. unit is dyne cm^{2}g^{-2}.

### Dimensions of G:

- The gravitational force between two point masses ‘m
_{1}’ and ‘m_{2}’ separated by distance ‘r; is given by

- Hence the dimensions of universal gravitation constant are [M
^{-1}L^{3}T^{-2}]

### Definition of G:

- The gravitational force between two point masses ‘m
_{1}’ and ‘m_{2}’ separated by distance ‘r; is given by

Let r = 1 unit, m_{1} = m_{2} = 1 unit, then G = F

- Hence, the universal gravitational constant is the numerical value of the force between two unit masses kept at a unit distance from each other.

### Newton’s Law of Gravitation in Vector Form:

### Weight of the Body:

- The weight of a body is the force with which body is attracted towards the centre of the earth.
- Its unit is newton (N) and dimensions [M
^{1}L^{2}T^{-2}] are the same as that of the force.

### Force of Gravitation:

- The force of attraction between two material bodies in the universe is known as the force of gravitation.
- If one of the body is the earth or some other planet or natural satellite then the force of gravitation is called the force of gravity.

### Notes:

- Gravitational force between two bodies is called action – at – a distance type of interaction, because the two particles interact even though they are not in contact with each other. Thus gravitational force is a non-contact force.
- Universal gravitational constant G is numerically equal to the force of attraction between two bodies each of unit mass, separated by a unit distance.
- The value of G is very small and gravitational forces are small unless the masses of the two attracting bodies are large.
- If the value of G becomes 100 times its present value, then earth’s attraction would be so large that we would be crushed to the earth.
- If the value of G becomes 1/100 times its present value, then we would be able to jump from multi-storey building.
- Principle of Superposition of Forces:

THIS CONTENT IS VERY GOOD FOR HIGH LEVEL EXAMS