For low-speed motion of a small sphere through a viscous fluid

PHYSICS · Single correct · CBSE · Physics · Mechanical Properties of Fluids · Mechanical Properties of Fluids

Problem

For low-speed motion of a small sphere through a viscous fluid, the drag force

F

is found to depend on the sphere's radius

r

, its speed

v

, and the dynamic viscosity of the fluid

\eta

. Which proportionality satisfies dimensional requirements? (a)

F \propto \eta r^{3} v^{-1}

(b)

F \propto \eta r^{2} v

(c)

F \propto \eta r v

(d)

F \propto \eta r v^{2}