If the diameter of the earth becomes two times its present value and its mass remains unchanged,then how would the weight of an object on the surface of the earth be affected?

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

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.

$A$ 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?

What will be the mass of a body at the centre of the earth as compared to other places on the earth?

Give an example of the motion of an object under the influence of gravitational force on Earth.