Question

What do you understand by gravity and acceleration due to gravity establish relationship between G and g

Answer 1

gravity is a force with which a body is attracted towards the centre of the earth.
when a body Falls freely under gravity then its velocity increases continuously which time at uniform rate and this increase in velocity is brought about by Gravity so it is called acceleration due to gravity.
since we know that weight is an effective force due to gravity.
and thus weight is the product of mass and acceleration due to gravity
mg=GMm/R²
g=GM/R²