Question

state the law of gravitation and write its mathematical experision

Answer 1

The force of Gravitational interaction between two points masses m1 and m2 is proportional directly to the product of the masses and inversely to the square of the distance between them. 
Thus, mathematically,

F=Gm1m2r2 where G is a constant and r is the separation between particles.

Also, the force acts along the line joining the particles.

Answer 2

Hi,

Here is your answer,

                                UNIVERSAL LAW OF GRAVITATION 

↔ It states that in everybody in the universe attracts each other body with a force whose magnitude is directly proportional to the product of their masses and inversely proportional to the square of the distances between their centers. This force acts along the line joining the centers of two bodies.

↔ Now, Let us consider tow bodies of masses m₁ and m₂ with their centers mutually separated by a distance r. Let F be the force(in magnitude) of gravitational attraction between two bodies.

According to Newtons's Law of gravitation

                Fα m₁ m₂ --------------------> (1)

and                  F α 1/r² --------------------------> (2)


Now from Eq (1) and (2)

                       F α m₁ m₂/r²

Or,     Gravitational force, F = G m₁ m₂/r² ----------------->(3)

↔ where G is a constant of proportionality knows as ''Gravitational constant'' . It is also known as universal gravitational constant.

↔ In CGS system the value of G is 6.67 × 10⁻⁸ dyne cm² g⁻²

→ It's SI unit is 6.67 × 10⁻¹¹ Nm² kg⁻²

⊕ DIMENSIONAL FORMULA OF G

        G = Fr²/ m₁ m₂ = [MLT⁻² ] [ L²]/[M²]

         = [MLT⁻² ] [L²] [M⁻² ]

          = [M⁻¹ L³ T⁻² ]


Hope it helps you !