Falling vertically in glycerine, a metal sphere has a mass of 50 mg and a radius of 1 mm . The coefficient of viscosity for glycerine at room temperature is 8.0 poise and its density is 1260 kg/m ^3 . Determine the viscous force exerted on the sphere by the glycerine when the sphere reaches a speed of 1 cm/s .

Step-by-step solution

The viscous force acting on a spherical body falling through a viscous medium is given by Stokes' law: F = 6 r v Given parameters are: Coefficient of viscosity, = 8.0 poise = 0.8 Pa s Radius of the sphere, r = 1 mm = 10⁻³ m Speed of the sphere, v = 1 cm/s = 10⁻² m/s Substituting the values into the formula: F = 6 3.14 0.8 10⁻³ 10⁻² F = 15.07 10⁻⁵ N F 1.5 10⁻⁴ N The mass of the sphere and the density of glycerine are extraneous information for finding the viscous force at a specific speed.