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

Answer: (b). Stokes' law: F = 6πη R v. For a given fluid, F ∝ R and F ∝ v. So the answer is (b) directly proportional to both R and v.

Spherical balls of radius R are falling in a viscous fluid of… | JEE Main 2004 (AIEEE)

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Viscosity & Stokes' Law

Spherical balls of radius $R$ are falling in a viscous fluid of viscosity $\eta$ with a velocity $v.$ The retarding viscous force acting on the spherical ball is

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Answer: (b)

Stokes' law: $F = 6\pi\eta R v$ .
For a given fluid, $F \propto R$ and $F \propto v$ .
So the answer is (b) directly proportional to both $R$ and $v$ .

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