Let’s start with the introduction of the Definition of Gravitational force and all-important terms related to the gravitation chapter.
Gravitation is the force of attraction between any two objects in the universe. All the bodies in the universe attract each other with a certain amount of force, but in most cases, the force is too weak to be observed due to the large distance of separation.
- Rain falls down from the sky to the earth due to the gravitational force of earth or gravity.
- If a ball is thrown upwards, it reaches a certain height and falls downwards because of the gravity of the earth.
Every-body in the universe attracts every other body
Force of attraction was first observed by Sir Isaac Newton and presented as Newton’s law of gravitation.
According to Newton, everybody in this universe attracts every other body with a certain force. The force with which two objects attract each other is called gravitational force.
If the masses of the objects are small, then the gravitational force between them is very small (which cannot be detected easily).
If one of the objects is big having a very large mass, then the gravitational force becomes very large and its effect can be seen easily.
Definition of Gravitational force
Each body in this universe attracts other bodies toward itself with a force known as Gravitational force. Out of the two masses, the heavier mass is called source mass and the lighter mass is called test mass.
The universal law of Gravitation
Newton said that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
F ∝ m 1 x m 2
F ∝ 1 / r 2
F ∝ m 1 x m 2 /r 2
where α is proportional symbol
F = G x m 1 x m 2/ r 2
F = gravitational force
m 1 = mass of 1st object
m 2 = mass of 2nd object
G = gravitational constant
r = distance between two objects
G = 6.67 X 10-11 Nm 2 / kg 2
Mass of Earth, M = 6 x 1024 kilogram
Radius of Earth,R = 6.4 x 106 metre
SOME IMPORTANT FACTS ABOUT GRAVITATION
- Gravitation is called the 4th law of Newton.
- Gravitational forces are weak and attractive forces.
- Gravitational force is valid for all distances (short and long)
- The value of ‘G’ is determined by Henry Cavendish.
- When two objects are dropped from the same height in a vacuum, they strike at the same time on the surface of the earth irrespective of their masses.
The space surrounding material objects within its gravitational force of attraction can be experienced is called its gravitational field. Two bodies attract each other by the gravitational force even when they are not in direct contact. It can be best explained in terms of the concept of field. According to this field concept,
• Every mass modifies the space around it. That modified space is called the gravitational field.
• If any other mass is placed in this field, it feels a gravitational force of attraction due to its interaction with the gravitational field.
The intensity of Gravitational Field
The gravitational field intensity at any point in the gravitational field due to a given mass is defined as the force experienced by a unit mass that does not disturb the original gravitational field.
Gravitational Potential Energy
It is the energy associated with it due to its position in the gravitational field of another body and is measured by the amount of work done in bringing a body from infinity to a given point in the gravitational field of the other. When one body lies at infinity from another body, the gravitational force on it is zero. Consequently, its potential energy is zero. This is called the zero level of potential energy.
It is the potential energy associated with a unit mass due to its position in the gravitational field of another body.
Gravitational Potential, V = Work Done/Mass = W/m
• It is a Scalar quantity.
• Its SI unit is J/Kg.
• The dimensional formula of gravitational potential = [ M0L2T-2].
The mass of a body that determines the gravitational pull due to earth acting upon it is called its gravitational mass.
F = GMmg/R2
Where Gravitational mass, mg = FR2/GM
Comparison between Inertial and Gravitational Masses
• Both represent the quantity of matter in a body.
• Both are equivalent in magnitude and have the same units of measurement.
• Both do not depend on the shape and state of matter.
• Both are not affected by the presence of other bodies.
• Both are scalar quantities.
• Inertial mass is the measure of the difficulty of accelerating a body while gravitational mass measures the force of attraction between the body and the earth.
• Inertial mass is determined from Newton’s second law of motion while gravitational mass is determined from Newton’s law of gravitation.
• Inertial masses can be measured only under dynamic conditions i.e. when the body is in motion. Gravitational mass can be easily measured by using a common balance.
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