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.

Which of the following is the evidence to show that there must be a force acting on the earth and directed towards the sun?

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

$A$ ball thrown up vertically returns to the thrower after $6 \, s$. Find:
$(a)$ The velocity with which it was thrown up.
$(b)$ The maximum height attained. (Take $g = 9.8 \, m s^{-2}$)

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.

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