Question

derive the formula F = G*M1 *m2 / r²

Answer 1

Derivation-

Acc. to the Newton’s Law of Gravitation,

The Gravitational Force between any two masses is inversely proportional to the square of distance between their centers and directly proportional to the product of their masses

Let us

Consider two masses of mass “m₁” and “m₂” And Let the distance them between their center be “r”

According to the Newtons law;

Force is inversely proportional to the square of distance between their centers,

F ∝ 1/r²    [ Eq. 1 ]

And Force is directly proportional to the product of their masses,

F∝ m₁ m₂    [ Eq. 2 ]

By equating two equations we get,

F∝ m₁ m₂/r²

To remove proportionality sign we added a constant G i.e. Gravitational constant.

F= G (m₁ m₂)/r²

where, G = Gravitational constant

∴ HENCE PROVED