Velocity of small ball of mass m and density ρ when dropped in a container filled with glycerine of

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9-1.Fluid Mechanics

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The velocity of small ball of mass $m$ and density $\rho $ when dropped in a container filled with glycerine of density $\sigma $ becomes constant after sometime. The viscous force acting on the ball in the final stage is

A

$mg\left( {\frac{\sigma }{\rho }} \right)$

B

$mg\left( {1 + \frac{\sigma }{\rho }} \right)$

C

$mg\left( {1 - \frac{\sigma }{\rho }} \right)$

D

$mg$

Solution

$\mathrm{F}_{\mathrm{v}}=\mathrm{mg}-\mathrm{Th}$

$=\operatorname{mg}\left(1-\frac{\mathrm{Th}}{\mathrm{mg}}\right)$

$=\operatorname{mg}\left(1-\frac{\mathrm{v} \sigma \mathrm{g}}{\mathrm{v} \rho \mathrm{g}}\right)$

$=\mathrm{mg}\left(1-\frac{\sigma}{\rho}\right)$

Standard 11

Physics

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