If a planet existed whose mass and radius were both half that of the Earth,the acceleration due to gravity at its surface would be: (in $, m s^{-2}$)

$A$ stone is dropped from the roof of a building. It takes $4 \, s$ to reach the ground. Find the height of the building. $(g = 9.8 \, m \, s^{-2})$

Two stones $A$ and $B$ are dropped from a multi-storey building. Stone $A$ is dropped from $100 \, m$ and at the same time stone $B$ is dropped from $50 \, m$ height. Both of them reach the earth at the same time. Will they have equal velocity while reaching the ground? Calculate and find out the answer (Take $g = 10 \, m s^{-2}$).

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.

$A$ 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 $g = 9.8 \, m s^{-2}$)

When dropped from the same height,a body reaches the ground quicker at the poles than at the equator. Why?