State whether the following statement is True or False:
The acceleration of a body thrown vertically upward is numerically the same as the acceleration of a body falling downward,but opposite in sign.

$A$ man weighs $600\,N$ on Earth. What is his mass? $(g=10\,m s^{-2})$. On the Moon,his weight would be $100\,N$. What is the acceleration due to gravity on the Moon?

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

$(i)$ How is the force of attraction dependent on the masses of objects and the distance between them?
$(ii)$ The mass of the Earth is $6 \times 10^{24} \, kg$ and that of a natural satellite is $6.5 \times 10^{20} \, kg$. If the distance between them is $3.35 \times 10^{6} \, km$, calculate the force exerted by the Earth on it. $(G = 6.7 \times 10^{-11} \, Nm^{2} kg^{-2})$

Write three differences between gravitational acceleration $(g)$ and gravitational constant $(G).$

$A$ ball is thrown vertically upwards with a velocity $u$. Calculate the velocity with which it falls to the earth again.