$A$ man at the top of a tower throws an object horizontally,whereas he simply drops another. Will these two objects reach the earth at the same time?

The equation $F = G \frac{m_1 m_2}{r^2}$ is valid only for:

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.

State whether the following statement is True or False:
All objects attract each other along the line joining their centre of mass.

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

Give reasons:
$(i)$ What is meant by acceleration due to gravity?
$(ii)$ The value of $g$ is not constant on the surface of the Earth.
$(iii)$ Objects of different masses take the same time to fall from a fixed height.
$(iv)$ $G$ is known as the universal gravitational constant. Write its $SI$ unit.