Question

Deduce a relation between g and G

Answer 1

G' & ‘g' are related to gravitational force.
G is known as universal gravitational constant. Its numerical value is 6.67 × 10^-11 N-m²/Kg²
g is known as acceleration due to gravity. And its generally numerical value is 9.8 m/s². It is changeable. It is different for place in earth. g = 10 m/s² in Poles.
The relation between ‘G’ & ‘g' :-
According the Newton’s law of gravitation -

F = G M.m / r² -(I)
where M and m are two masses distance between r metre.
By Newton's second law :-
F = mg -(ii)
Where F is force and m is mass and g is acceleration due to gravity.
Now equating equation (i) and (ii) than:-
= mg = G M.m / r²
= g = G M / r² -(iii)
The above equ. (iii) is the relation between ‘G’ and ‘g'.

Answer 2

Let us consider a body of mass m placed on the surface of the earth.
So, acc. to newton's second law of motion.
F = mg ———------ ( i )
Using gravitational force
F = Gm1me/r2 ———----- ( ii )
Equating ( i ) & ( ii )
mg = Gm1me/r2
g = Gme/re2
Where ‘me’ is the mass of the earth & ‘re’
is the radius of the earth.
Hence acceleration due to gravity is independent of the mass of the object which is allow to fall and all objects fall towards the earth with the same acceleration.