** The universal law of gravitational force**

**Type of Natural forces in the universe:**

Do you know why are all of the things are arranged in a matrix of the universe? Why does the moon revolve around the earth, and the same the earth and other planets do around the sun. The whole of the universe from the microscopic level to the macroscopic level is bounded by different kinds of natural forces. The microscopic level involves the forces between the particles of the matter like nuclear forces, intermolecular forces, electrostatic forces, etc whereas in the macroscopic level the forces between two objects are studied like a magnetic force, gravitational force. The discovery of gravitational force is said to be discovered by a great Indian astronomer and mathematician Bhaskaracharya in the eleventh century although it is self-examined, explored and deeply explained by Sir Issac Newton in 16 th century. The most popular discovery of Newton was the universal law of gravitational force. The whole of the universe is governed by this universal law of gravitational force.

**NCERT Solutions Class 10 Science from chapter 1 to 16**

**Observations of gravitational force:**

Initially, Newton observed an apple fell on him while he was sitting under an apple tree on a beach, a thought created in his brain why did it pour down. He concluded to the fact that the earth attracts everything towards its side by its gravitational force, then his brain clicked towards the moon and observed that the same kind of force might be applied by the earth on the moon, that causes the moon to revolve around the earth, and sequentially one by one he discovered three equation of motion and laws of motion, etc.

**Verification of universal law of gravitational force:**

If there are two objects of the masses m and M in the universe, the gravitational force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

F ∝ m×M ……….(i)

F ∝ 1/d²………………(ii)

From (i) and (ii) we have

F ∝ m×M/d²

This equation is known as the universal law of gravitational force, in this equation, F is called the universal gravitational force due to which all the heavenly bodies suspended and moving with respect to each other in the space and are under the control of a balanced force.

Where G is constant of proportionality is known as the universal constant of gravitational force and its value is

**Verification of universal constant of gravitational force:**

The unit of the universal constant of the gravitational force is determined as follows.

Hence unit of universal constant of gravitational force is Nm²/kg² or

**The relationship between G and g:**

Let the mass of an object on the earth is m.

The force is (F) = product of mass and acceleration

Here the acceleration on the object by the earth gravity is = g

∴ F = mg……(i)

……..(ii)

From (i) and (ii) we have

Since the object is on the surface of the earth, the distance must be substituted by the radius of the earth because the mass of the earth is centered at the center of the earth.

Therefore the above equation will become

This is the relationship from which we can determine g,r, M or G if 3 physical quantities are given, then we can determine the unknown value whether it is g, M,r or G.

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