Question

what is universal law of gravitation

Answer 1

Newton's law of universal gravitation states that a particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Answer 2

Hi

Here is your answer,

Every body in this universe attracts each other with a force whose magnitude is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. This force acts along the line joining the centres of two bodies.

Now, consider two bodies of masses m₁ and m₂ with their centres mutually separated by a distance r. So, the force( in magnitude) of gravitational attraction between two bodies.

 According to Newton's Law of Motion:-

           F α m₁m₂ ----------------> (1)

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

From equation (1) and (2)

        F α m₁m₂/r²

 Gravitational force, F = G m₁m₂/r² ------------------->(3)

where G is constant of proportionality known 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 and its SI value is 6.67×10 Nm² kg⁻²

DIMENSIONAL FORMULA FOR G

       G= F r²/m₁m₂ = [ MLT⁻² ] [ L² ]/[M²]

       = [ MLT⁻² ] [L³ [ [ M⁻² ] 

       = [ M⁻¹ L ³T⁻² ]

Now suppose, m = m = 1 unit and r = 1 unit, then from Eq (3) 

      F = G ×1 ×1/(1)² = F = G

Thus, universal gravitational constant (G) is numerically equal to the force of attraction acting between two bodies each of unit mass by unit distance apart.



Hope it helps you !