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

(B) directly proportional to both radius R and velocity v .

(A) directly proportional to R but inversely proportional to v .

(C) inversely proportional to both radius R and velocity v .

(D) inversely proportional to $R$ but directly proportional to velocity $v$.

JEE Main · 2004 · 24 Apr 2004 · Offline · Fluid Mechanics

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)directly proportional to R but inversely proportional to v .
(B)directly proportional to both radius R and velocity v .✓ Correct
(C)inversely proportional to both radius R and velocity v .
(D)inversely proportional to $R$ but directly proportional to velocity $v$ .

Answer: (B)

Solution

By Stokes' law the viscous drag on a small sphere moving through a fluid is

F = 6 π η R v

. The force is therefore proportional to the radius of the sphere and to its speed together.

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option

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