Universal Law of Gravitation


 
 
Concept Explanation
 

Universal Law of Gravitation

The Universal Law of Gravitation:

The law was formulated by Newton. The gravitational force of attraction between any two particles in the universe is directly proportional to the product of the masses of the particles and is inversely proportional to the square of the distance between the particles. The direction of the force is along the line joining the two particles. Let A and B be two particles of masses m_1 and m_2  respectively. Let the distance AB = r. By the law of gravitation, the particle A attracts the particle B with a force F, such that 

F ∝ m_1m_2  (for a given separation between the particles)

F alpha frac{1}{r^2} (for; a ;given ;pair; of; particles).

So, Falpha frac{ m_1 m_2}{ r^2} or;; F = frac{G m_1 m_2}{ r^2}

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 X 10^{-11} Nm^2/ kg^2

Its value does not depend on the medium between the two bodies and the masses of the bodies or the distance between them. This law is universal as it is applicable to all bodies, whether the bodies are big or small, whether they are celestial or terrestrial. Suppose the masses of two bodies having 1 kg each and the distance d between them is 1 m, then

F= G [m_1  and m_2 = 1kg  and r = 1m]

Then, the universal gravitational constant is defined as the gravitational force between two objects of unit mass each separated by a unit distance from each other placed anywhere in space. The SI unit of G is

Nm^2/ kg^2

The value of G was found out by Henry Cavendish (1731-1810) by using a sensitive balance.

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Sample Questions
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Question : 1

As one moves away from the earth's surface

Right Option : A
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Question : 2

The force of gravitation between two objects of masses 1 Kg and 2 Kg separated by a distance of 100 cm, is

Right Option : A
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Question : 3

If earth attracts an object towards its centre with the force of 500 N, the force of attraction exerted by the object on earth is

Right Option : C
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