Define and derive universal law of …

According to the universal law of gravitation, every object in the universe attracts every other object with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them. The direction of force is along the line joining the centres of the two bodies.

This law was given by Sir Isaac Newton.

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.