The force of gravitation between two bodies varies with the distance $r$ as:

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

$(a)$ What do you mean by free fall?
$(b)$ What happens to the direction of motion of objects during free fall?
$(c)$ $A$ stone is dropped from a height of $19.6 \, m$. Calculate:
$(i)$ Time taken to fall.
$(ii)$ How fast does it move at the end of this fall?
$(iii)$ Acceleration after $1 \, s$.

Show that the weight of an object on the moon is one-sixth of its weight on the earth. [Given: mass of earth $= 5.98 \times 10^{24} \ kg$,mass of moon $= 7.36 \times 10^{22} \ kg$,radius of earth $= 6.37 \times 10^{6} \ m$,radius of moon $= 1.74 \times 10^{6} \ m$]

Give a reason for the statement that the value of $g$ is greater at the poles than at the equator.

When a spaceship is two earth radii distant from the centre of the earth,its gravitational acceleration is: (in $, m s^{-2}$)