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

Question

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 (C) inversely proportional to R but directly proportional to velocity v (D) inversely proportional to R but directly proportional to velocity v

Tardigrade Admin · Accepted Answer

Retarding force acting on a ball falling into a viscous fluid

F = 6 π η R v

where

R

= radius of ball,

v

= velocity of ball and

η =

coefficient of viscosity

∴ F \propto R

and

F \propto v

Or in words, retarding force is directly proportional to both

R

and

v

.

Q. 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

directly proportional to R but inversely proportional to v

directly proportional to both radius R and velocity v

inversely proportional to R but directly proportional to velocity v

inversely proportional to R but directly proportional to velocity v

Retarding force acting on a ball falling into a viscous fluid F=6πηRv where R = radius of ball, v = velocity of ball and η= coefficient of viscosity ∴F∝R and F∝v Or in words, retarding force is directly proportional to both R and v.

Q. 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

Retarding force acting on a ball falling into a viscous fluid
$F = 6 π η R v$ where
$R$ = radius of ball,
$v$ = velocity of ball and
$η =$ coefficient of viscosity
$∴ F \propto R$ and $F \propto v$
Or in words, retarding force is directly proportional to both $R$ and $v$ .