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 both radius R and velocity v.

inversely proportional to R but directly proportional to velocity v.

Solution

directly proportional to both radius R and velocity v.

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

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Mechanical Properties Of Fluids

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