Question

Derive formula of universal law of gravitation.

Answer 1

 Derivation:  

Say FG is the force of gravitational attraction between any two objects,

m1 is the mass of one object,

m2 is the mass of a second object,

d is the distance between the centers of the two objects. (Objects are assumed to be spherical.)

newton's law of universal gravitation

Now as said in the Law of Gravitation:

FG ∞ m1.m2

and

        FG ∞  1/d2

So,   FG ∞ m1.m2/ d2

        FG = (G.m1.m2)/ d2

G is a constant which is discussed in the next section.

This equation gives us the expression of the gravitational force.

Answer 2

Given :

Universal law of gravitation.

To Find :

Derive the formula of universal law of gravitation.

Solution :

Any two particles in the universe attract each other along a straight line joining them. The magnitude of the force of attraction is directly proportional to the product of the masses of these two particles and is inversely proportional to the square of the linear distance between them.

Let the two particles of masses m₁ and m₂ kept 'r' distance from each other. If the force of attraction between them is F, then as per Newton's law of Gravitation,

                 F $\alpha$ m₁m₂   (when r remains constant)

                  F $\alpha$ $\frac{1}{r^2}$         (when m₁ and m₂ remain unchanged)

Hence,       F $\alpha$ $\frac{m_1m_2}{r^2}$

or,               F = $\frac{Gm_1m_2}{r^2}$

G is called the universal gravitational constant.

Value of G in SI unit is 6.67 × $10^{-11}$ N . m² . $kg^{-2}$

Hence, the formula of Universal law of Gravitation is F =  $\frac{Gm_1m_2}{r^2}$.