Assume a spherical ball $($diameter D$,$ density p$)$ is falling through air $($density Pa$)$ under the action of gravity.

a$)$ Find out the acceleration of the ball based on the forces acting on it$.$

b$)$ Write the mathematical form of the Stoke's law for the drag force for a sphere explaining all the terms clearly.

c$)$ What do you understand by terminal velocity?

d$)$ Derive the expression of terminal velocity for the ball.

e$)$ At what range of Reynolds number Stoke's law is valid?