What is the importance of the universal law of gravitation?

$(a)$ Differentiate between $G$ and $g$.
$(b)$ Is the value of $g$ the same everywhere on Earth? Reason out.
$(c)$ How does the gravitational force between two objects change if the distance between them is tripled?

$(a)$ The Earth is acted upon by the gravitation of the Sun,yet it does not fall into the Sun. Why?
$(b)$ An object of mass $500 \, g$ is dropped from a tower of height $5 \, m$. Calculate its momentum when it touches the ground (given $g = 10 \, m s^{-2}$).

The gravitational force between two objects is $F$. How will this force change when:
$(i)$ the distance between them is reduced to half?
$(ii)$ the mass of one of the objects becomes four times?

How does the force of attraction between two bodies depend upon their masses and the distance between them? $A$ student thought that two bricks tied together would fall faster than a single one under the action of gravity. Do you agree with his hypothesis or not? Comment.

$(a)$ Prove that if the Earth attracts two bodies placed at the same distance from the center of the Earth with equal force,then their masses will be the same.
$(b)$ Mathematically express the acceleration due to gravity experienced by a free-falling object.
$(c)$ Why is $G$ called a universal gravitational constant?