The force of gravitation between two bodies varies with the distance $r$ as:

On the Earth,a stone is thrown from a height in a direction parallel to the Earth's surface,while another stone is simultaneously dropped from the same height. Which stone would reach the ground first and why?

$(a)$ 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?

The gravitational force between objects is $100 \, N$. How should the distance between these objects be changed so that the force between them becomes $50 \, N$?

$(a)$ $A$ cube of side $5\, cm$ is immersed in water and then in a saturated salt solution. In which case will it experience a greater buoyant force? If each side of the cube is reduced to $4\, cm$ and then immersed in water,what will be the effect on the buoyant force experienced by the cube as compared to the first case for water? Give reasons for each case.
$(b)$ $A$ ball weighing $4\, kg$ with a density of $4000\, kg\, m^{-3}$ is completely immersed in water of density $10^3\, kg\, m^{-3}$. Find the force of buoyancy on it. (Given $g = 10\, m\, s^{-2}$)

If the distance between two objects is doubled,the gravitational force between them :