Derive the Relation between g and G .

Explanation

(i) Let , M be the mass of the Earth and m be the mass of the object .
(ii) The entire mass of the Earth is assumed to be concentrated at its centre . The radius of the Earth is R (=6378 km=6400 km approximately ).
(iii) By Newton's law of gravitation , the force action on the object is given by
`F=GM m//R^(2)` ......... (A)
(iv) According to Newton second law , the force acting on the object is given by the product of its mass and acceleration . Here acceleration of the is under the action of gravity hence a=g .
F=ma=mg
F= weight = mg ..........(B)
Comparing equations (A) and (B) , we get
mg= GM`m//R^(2)`
Acceleration due to gravity
`g=(GM)/(R^(2))`