Question

derive an expression That Give relation 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

G stands for Newton's universal gravitational constant, whereas g stands for the acceleration due to gravity at a certain point.

G = 6.67300 × 10-11 http://N.m2.kg-2, G is a constant throughout space and time and it is a scalar quantity.

g = 9.8 m.s

-2

, g is acceleration due to gravity which is a variable quantity and a vector qualtity.

According to Newton's law of universal gravitation the force of attraction between two bodies is given by

F = GMm/r

2

---------- (i)

From Newton's second law of motion the weight of a body of mass m is

F = mg -----------------(ii)

From (i) and (ii)

mg = GMm/r

2

or

g = GM/r

2

Note:

g is a constant at a given location, which depends upon M and r.

You can understand it more by this

Hope this will help u