A small aluminum ball with D = 2 mm and s = 2700 kg/m 3 is

A small aluminum ball with D = 2 mm and ρ_s = 2700 kg/m³ is dropped into a large container filled with oil at 40°C (ρf = 876 kg/m³ and μ = 0.2177 kg/m·s). The Reynolds number is expected to be low and thus Stokes law for drag force F_D = 3πμDV to be applicable. Show that the variation of velocity with time can be expressed as V = (a/b)(1 – e^–bt) where a = g(1 – ρ_f/ρ_s) and b = 18μ/(ρ_sD²). Plot the variation of velocity with time, and calculate the time it takes for the ball to reach 99 percent of its terminal velocity.