A ball is dropped from rest from the top of a building. what force is responsible for the downward motion of the ball?

When a ball is dropped from building, it will experience two forces: gravitational force (acting in downward direction) and air resistance (acting in upward direction i. e opposite to the motion of ball). This air resistance can be neglected because coefficient of viscosity of air is very less. So only gravitational force is responsible for downward motion of the ball.

The force responsible for the downward motion of the ball is the force that

Sir Isaac Newton named "Universal Gravitation" about 300 years ago.

The name has stuck, although we did shorten it, and we just call it 'Gravity'.