How the value of constant G …

Suppose two bodies A and B of masses M and m are lying at a distance d from each other. Let the force of attraction between these two bodies be F. according to the universal law of gravitation;

1. The force between the two bodies is directly proportional to the product of their masses.

F ∝ M × m

1. The force between the two bodies is inversely proportional to the square of the distance between them.

F ∝ 1/d²

Combining both the equations:

F ∝ M x m/d²

Or F = G M x m/d²                                                                                         i.

where G is the constant of proportionality and is called the universal gravitation constant.

By multiplying crosswise we get

 F × d² = G M × m

Or G = F d²/ M x m

The SI unit of G can be obtained by substituting the units of force, distance and mass as N m² kg ^–2.

The value of G was found out by Henry Cavendish (1731 – 1810). The accepted value of G is 6.673 × 10^–11 N m² kg^–2.