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Calculate the magnitude and direction of the terminal velocity of an air bubble of radius $1\;mm$ passing through an oil viscosity $0.2\;N\,s\, /m^2$ and specific gravity $0.9$ if the density of air is $1.29\;kg/m^3$.

Castor oil at $20^{\circ}\;C$ has a coefficient of viscosity $2.42\;N\,s\, /m^2$ and density $940\; kg/m^3$. Calculate the terminal velocity of steel ball of radius $2\;mm$ falling under gravity in the oil, taking density of steel as $7800\;kg/m^3$.