State the universal law of gravitation and derive its mathematical expression .

Explanation

This law states that every particle of matter in this universe attracts every other particle with a force. This force is directly proportional to the product of their masses and inversely proportional to the square of the distance between the centers of these masses. The direction of the force acts along the line joining the masses.

Force between the masses is always attractive and it does not depend on the medium where they are placed.
Let, `m_(1) and m_(2)` be the masses of two bodies A and B placed r metre apart in space.
Force `" "F prop m_(1)xxm_(2)`
`F prop 1//r^(2)`
On combining the above two expressions
`F prop (m_(1)xxm_(2))/(r^(2))`
`F=(Gm_(1)m_(2))/(r^(2))`
Where G is the universal gravitational constant. Its value of SI unit is `6.674xx10^(-11)Nm^(2)kg^(-2)`.