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  • In Millikan’s oil drop experiment, what is the terminal speed of an uncharged drop of radius 2.0 × 10^–5 m and density 1.2 × 10^3 kg m^–3. Take the viscosity

Q 10.28 In Millikan’s oil drop experiment, what is the terminal speed of an uncharged drop of radius 2.0 × 10-5 m and density 1.2 × 103 kg m-3. Take the viscosity of air at the temperature of the experiment to be 1.8 × 10-5 Pa s. How much is the viscous force on the drop at that speed? Neglect buoyancy of the drop due to air.

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Neglecting buoyancy due to air the terminal velocity is

\\v_{T}=\frac{2}{9}\frac{r^{2}\rho g}{\eta }\\ v_{T}=\frac{2\times (2\times 10^{-5})^{2}\times 1.2\times 10^{3}\times 9.8}{9\times 1.8\times 10^{-5}}\\ v_{T}=5.807\times 10^{-2}\ m\ s^{-1}

Viscous Force Fv at this speed is

\\F_{v}=6\pi \eta rv_{T}\\ F_{v}=6\pi \times 1.8\times 10^{-5}\times 2\times 10^{-5}\times 5.807\times 10^{-2}\\ F_{v}=3.94\times 10^{-10}N

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