Question

the viscous force acting on a solid ball moving in air with terminal velocity v is directly proportional to

Answer 1

According to stoke's law, when a solid ball of radius R is moving in air with terminal velocity v and coefficient of viscosity is η , then viscous force is given by
F = 6πηRv
F$\propto$R and F$\propto$V

Form above it is clear that viscous force is directly proportional to terminal velocity and radius of object ( ball).

Answer 2

According to stoke's law , when an object rises or falls through fluid it experiences a viscous drag .

Formula :Frictional force [F]=6πηRv 

where v= terminal velocity
η=coefficient of viscosity.
R=radius of ball moving in air

we can say from Stoke's law :
 Viscous force is directly proportional to Terminal velocity and Radius of object.