Question

A metal ball is falling with terminal velocity in a liquid. If we change the radius of ball, how the viscous drag force, acting on the ball, will change?
1. F ∝ r²
2. F ∝ 1/r
3. F ∝ 1/r²
4. F ∝ r

Answer 1

Correct Answer - Option 4 : F ∝ r

CONCEPT: 

• Viscosity: The state of being sticky, thick, and semi-fluid inconsistency, due to internal friction of fluids is called viscosity.
• Stokes Law: This law tells about the viscous drag force when a sphere goes with a terminal velocity v inside a liquid.

By this law viscous drag force is given by:

F = 6πηrv

where r is the radius of the sphere, v is the velocity, and η is the viscosity of the fluid.

EXPLANATION:

The viscous drag force is given by:

F = 6πηrv

So F ∝ r

Hence the correct answer is option 4.