If the density of a planet is doubled without changing its radius,how does $g$ on the planet change?

State whether the following statement is True or False:
The acceleration due to gravity $g$ is given by the formula $g = GM/R^2$,where symbols have their usual meanings.

Define 'acceleration due to gravity of earth'. Does the acceleration produced in a freely falling body depend on the mass of the body? Justify your answer mathematically.

The acceleration due to gravity at the moon's surface is $1.67 \, m s^{-2}$. If the radius of the moon is $1.74 \times 10^{6} \, m$,calculate the mass of the moon. (Use $G = 6.67 \times 10^{-11} \, N m^{2} kg^{-2}$)

$A$ 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?

Prove that if a body is thrown vertically upward,the time of ascent is equal to the time of descent.