$A$ ball is thrown vertically upward,acceleration due to gravity is:

State Newton's universal law of gravitation and write an expression for it. Also,show that the acceleration due to gravity of an object is independent of its mass.

All the planets are moving in circular orbits. What provides the necessary force for this motion and what is the direction of this force? What will happen if this force disappears suddenly?

$A$ man throws a ball of mass $0.5 \, kg$ vertically upward with a velocity of $25 \, m s^{-1}$. Find: $(a)$ the initial momentum of the ball,$(b)$ the momentum of the ball at the halfway mark of the maximum height. (Given $g = 10 \, m s^{-2}$)

The value of $g$ on the earth's surface is $9.8 \, m s^{-2}$. Suppose the earth suddenly shrinks to one-third of its present size without losing any mass. What is the value of $g$ on the surface of the shrunk earth (in $, m s^{-2}$)?

$(a)$ 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?