The Question is from neet-physics mechanical-properties-of-fluids , and it was created by the author P.NARASIMHA

Question

Which of the following factors does *not* directly affect the viscous force acting on a spherical object moving through a viscous fluid according to Stokes' Law?

P.NARASIMHA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: D
## CONCEPT FRAMEWORK
 **Primary Concept**: Stokes' Law
 **Related Topics**: Fluid dynamics, viscosity, drag force
 **Prerequisites**: Understanding of viscosity and drag forces.
## SOLUTION PATHWAY
**Given Information**:
The question asks which factor does *not* affect the viscous force according to Stokes' Law.
**Method & Steps**:
Stokes' Law describes the settling of spherical particles in a fluid.  The formula is:
1. $F_d = 6πηrv$
where:
$F_d$ is the drag force (viscous force)
$η$ is the dynamic viscosity of the fluid
$r$ is the radius of the spherical object
$v$ is the velocity of the object
From the equation, we can see that the drag force ($F_d$) is directly proportional to the radius ($r$), viscosity ($η$), and velocity ($v$).
2. The density of the object ($ho$) is not directly included in Stokes' Law. While the density influences the buoyant force acting on the object (Archimedes' principle), it does not directly affect the viscous drag force itself. The buoyant force affects the *net* force on the object, but not the viscous force.
3. Therefore, the density of the object does not directly affect the viscous force.
  Result: The density of the object does not directly affect the viscous force according to Stokes' Law.
  Verification: The formula of Stokes' law itself shows that only radius, velocity and viscosity of fluid are involved.
 ## OPTION ANALYSIS
A :x: Radius of the object directly affects the viscous force according to Stokes' Law. 
B :x: Velocity of the object directly affects the viscous force according to Stokes' Law.
C :x: Viscosity of the fluid directly affects the viscous force according to Stokes' Law.
D ✓: Density of the object does not directly affect the viscous force; it affects the buoyant force, which is a separate force.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Confusing buoyant force with viscous drag force:  Students may mistakenly think that density influences viscous drag because a denser object experiences a larger net downward force.
  How to avoid: Carefully distinguish between buoyant force (related to density and fluid displacement) and viscous drag force (related to viscosity, velocity, and object size).
  2.Incorrectly applying Stokes' Law to non-spherical objects: Stokes' Law is specifically derived for spherical objects. For other shapes, the drag force equation becomes more complex.
  How to avoid: Ensure the object is spherical before applying Stokes' Law.
 **Quick Tips**:
  1.Memorize Stokes' Law equation:  This will quickly identify the factors that directly influence the viscous drag force.
  2.Focus on the definition of viscous force:  Viscous force is the resistance to motion due to the fluid's internal friction. Density doesn't directly participate in this friction.

P.NARASIMHA · Answer

Radius of the object

P.NARASIMHA · Answer

Velocity of the object

P.NARASIMHA · Answer

Viscosity of the fluid

P.NARASIMHA · Answer

The correct Option is "Density of the object"

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