$A$ stone is dropped from a cliff. Its speed after it has fallen $100 \,m$ is: (in $, m s^{-1}$)

Show mathematically that the acceleration experienced by an object during free fall is independent of the mass of the object.

The weight of an object at the centre of the earth of radius $R$ is

Distinguish between mass and weight of an object. How does the weight of an object change when moving from the equator to the poles? When can the weight of an object be zero?

State whether the following statement is True or False:
The centre of mass and centre of gravity for a small body lie at the same point.

Find the weight of an object at a height $6400 \, km$ above the earth's surface. The weight of the object at the surface of the earth is $20 \, N$ and the radius of the earth is $6400 \, km$. (in $, N$)