Spherical balls of radius R are falling in a viscous fluid...

Spherical balls of radius $R$ are falling in a viscous fluid of velocity $v$. The retarding viscous force acting on the spherical ball is (a) directly proportional to $R$ but inversely proportional to $v$. (b) directly proportional to both radius $R$ and velocity $v_{.}$ (c) inversely proportional to both radius $R$ and velocity $v$ (d) inversely proportional to $R$ but directly proportional to velocity $v$

Spherical balls of radius $R$ are falling in a viscous fluid of velocity $v$. The retarding viscous force acting on the spherical ball is
(a) directly proportional to $R$ but inversely proportional to $v$.
(b) directly proportional to both radius $R$ and velocity $v_{.}$
(c) inversely proportional to both radius $R$ and velocity $v$
(d) inversely proportional to $R$ but directly proportional to velocity $v$

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Key Concepts

Stokes' Law

Stokes' Law provides the relationship between the drag force experienced by a spherical object moving through a viscous fluid and the object's dimensions and velocity. It states that the retarding force is directly proportional to the sphere's radius, the fluid's viscosity, and the velocity, making it particularly applicable in conditions of low Reynolds numbers where the flow is laminar.

Viscous Drag

Viscous drag refers to the force that resists an object’s motion through a fluid due to the fluid’s internal friction. This force is influenced by the fluid’s viscosity, the object's dimensions (such as radius in the case of a sphere), and the velocity at which the object moves through the fluid.

Laminar Flow and Reynolds Number

Laminar flow describes a smooth, orderly fluid motion typically observed at low velocities or in highly viscous fluids, where flow layers slide past one another with minimal mixing. The Reynolds number, a dimensionless parameter, helps determine whether a flow will be laminar or turbulent, and under laminar conditions, Stokes' Law effectively characterizes the viscous drag on objects.

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