Question

Derive the relation between 'g' and 'G'

Answer 1

We know, by the universal law of gravitation, that

F = GMm/R²

And also, by second law of motion,

F = ma
Since, g = acceleration due to gravity,
F = mg

Now, equating both, we get

mg = GMm/R²
Cancelling m from both sides, we get,

g = GM/R²
where g = acceleration due to gravity, G is universal gravitational constant, M is the mass of the planet, and R is the radius of the planet.

Hope this answer helps you. :-)