Question

Consider the following statement for a ball falling in a viscous fluid:

a) The viscous force is directly proportional to the radius of the ball

b) The viscous force is directly proportional to the velocity of the ball

c) The viscous force is inversely proportional to the radius of the ball

d) The viscous force is inversely proportional to the velocity of the ball

Which of the above statements are correct?

1. Both a and b are correct
2. Both a and d are correct
3. Both b and c are correct
4. Both c and d are correct

Answer 1

Correct Answer - Option 1 : Both a and b are correct

CONCEPT:

Stoke's law:

• When a body moves through a fluid, the fluid exerts a viscous force on the body to oppose its motion.
• When a spherical body of radius r is dropped in a viscous fluid, the viscous force acting on a sphere is directly proportional to the following parameters:
  • ​The radius r of the sphere
  • Viscosity η
  • The velocity v of the object
• ​The viscous force is given as,

⇒ F = 6πηrv

EXPLANATION:

• From the above, it is clear that the viscous force is directly proportional to the radius of the ball and to the velocity of the ball. Hence, option 1 is correct.