A sphere of mass M and radius R is falling in a viscous fluid. terminal velocity attained by falling

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9-1.Fluid Mechanics

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A sphere of mass $M$ and radius $R$ is falling in a viscous fluid. The terminal velocity attained by the falling object will be proportional to

A

$R^2$

B

$R$

C

$1/R$

D

$1/R^2$

Solution

For a falling body in viscous fluid the terminal velocity is related to radius as follows.

${{\rm{V}}_{\rm{T}}} = \frac{2}{{9\eta }}{{\rm{R}}^2}(\rho – \sigma ){\rm{g}} \Rightarrow {{\rm{v}}_{\rm{T}}} \propto {{\rm{R}}^2}$

Standard 11

Physics

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