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 hydrostatic force exerted on the sphere by the glycerine.

Step-by-step solution

The hydrostatic force exerted by the fluid on the sphere is the buoyant force acting on it. The formula for buoyant force is given by: F_B = V g Where: V is the volume of the sphere = 4 3 r^3 is the density of the fluid (glycerine) = 1260 kg/m ^3 g is the acceleration due to gravity = 9.8 m/s ^2 r is the radius of the sphere = 1 mm = 10⁻³ m Substituting the values into the formula: F_B = 4 3 (10⁻³)^3 1260 9.8 F_B = 4 3 22 7 10⁻⁹ 1260 9.8 F_B = 4 22 60 9.8 10⁻⁹ F_B = 5280 9.8 10⁻⁹ F_B = 51744 10⁻⁹ N F_B = 5.1744 10⁻