The gravitational force between two objects is $F$. If the masses of both objects are halved without changing the distance between them,then the gravitational force would become:

In the relation $F = G \frac{Mm}{d^2}$,the quantity $G$:

$A$ 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 $g = 10 \, m s^{-2}$)

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.

An object is thrown vertically upwards and rises to a height of $10 \, m$. Calculate:
$(i)$ the velocity with which the object was thrown upward and
$(ii)$ the time taken by the object to reach the highest point.

$(i)$ Is the acceleration due to gravity of earth '$g$' always a constant at every place? Discuss.
$(ii)$ During a free fall,will heavier objects accelerate more than lighter ones? Give reason for your answer.