A spherical particle falling at a terminal speed in a liquid must have the gravitational force balanced by the drag forc

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A spherical particle falling at a terminal speed in a liquid must have the gravitational force balanced by the drag force and the buoyant force. The buoyant force is equal to the weight of the displaced fluid, while the drag force is assumed to be given by Stokes Law, 𝐹s=6𝜋𝑟𝜂𝑣.Fs=6πrηv. Show that the terminal speed is given by 𝑣=2𝑅2𝑔9𝜂(𝜌s−𝜌1)v=2R2g9η(ρs−ρ1) R is the radius of the sphere, 𝜌sρs is its density, and 𝜌1ρ1 is the density of the fluid, and 𝜂η