Question

derive the relationship between G and g

Answer 1

Gravitational force is given by
F = GMm/r^2

Here F = ma = mg

Therfore,
mg = GMm/r^2
Divide both sides by m
g = GM / r^2

In above g and G relation
g = acceleration due to gravity of planet
G = universal gravitational constant
M = mass of planet
r = radius of planet

Answer 2

HII
BRAINLY HERE TO HELP YOU ^_^

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Let us Derive the relationship between
G (Universal Gravitational Constant) & g (Acceleration due to gravity)

According to Newton's Gravitational Law,
Force = G Me m / R^2.
where Me = Mass of Planet; m = Mass of body ; R = Distance of separation or radius of earth

F = GMem / R^2 --------(I)

And According to Newton's Second law
F = mass × acceleration

F = m × a ---------- (II)
( a can be replaced by g because both are acceleration)

COMBING (I) & (II)

GMem / R^2. = m g
m will cancel out

=> GMe / R^2 = g

=> g = GMe / R^2
Acceleration due to gravity = Universal gravitational constant × mass of planet / square of distance of separation or radius of planet

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
THEREFORE, RELATION BETWEEN G & g will be

g = GMe / R^2

OR

G = g × R^2 / Me

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

VALUE OF UNIVERSAL GRAVITATIONAL CONSTANT IS ALWAYS CONSTANT WITH RESPECT TO PLACE i.e. IT IS THE SAME ALL OVER THE UNIVERSE AND ITS VALUE IS

G = 6.67 × 10 ^(-11) Nm^2kg^(-2)

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HOPE IT HELPS :):):):):):):):):):)