Question

state and prove universal law of gravatation
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Answer 1

Answer:

Gravitation, also known as gravity, is a force that exists among all material objects in the universe. Gravity acts on objects of all sizes ranging from subatomic particles to cluster of galaxies. Sir Issac Newton studied its behaviour with his famous law of gravitation. In physics, gravitation is defined as the force that attracts every object to the centre of gravity. In general, gravitation is the force exerted by the body due to the virtue of its mass.

The Universal Law of Gravitation can be stated as:

“Every object of mass in the Universe attracts every other object of mass with a force which is directly proportional to the product of their masses and inversely proportional to the square of the separation between their centres.”

In this article, let us learn more about the universal law of gravitation.

Newton’s Law of Universal Gravitation

According to the Universal law of gravitation, the force between two bodies is directly proportional to their masses and inversely proportional to the square of the distance between them. Mathematically, it is represented as follows:

F∝m1m2r2⇒F=Gm1m2r2

where,

F is the gravitational force between two bodies

m1 is the mass of one object

m2 is the mass of the second object

r is the distance between the centers of two objects

G is the Universal Gravitation Constant.

Henry Cavendish, with careful experiments, found the value of Gravitational Constant to be 6.67 x 10−11 m3⋅kg−1⋅s−2N. The value of ‘G’ remains constant throughout the universe.

Answer 2

Universal Law of Gravitation ;

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The gravitational force of attraction between any two particles is directly proportional to the product of the masses of the particles and is inversely proportional to the square of distance between the particles. The direction of the force is along the line joining the two particles.

And,

Now , adding ( 1 ) and ( 2 ), we get ;

Or ,

Here, G is a constant known as the universal constant of Gravitation. The value of G was experimentally measured in the laboratory by Cavendish, long after Newton's death. This value is

G = 6.67 × 10 ^ - 11 Nm² / kg².