A small glass marble falls through a column of liquid having a viscosity of 0.2 Pa s . If the instantaneous velocity of the marble is 0.5 m s ⁻¹ and the viscous drag force acting on it is 6 10⁻⁴ N , what is the diameter of the marble?

Step-by-step solution

According to Stokes' law, the viscous drag force acting on a spherical body is given by: F_v = 6 r v Substituting the given values: 6 10⁻⁴ = 6 0.2 r 0.5 Cancelling 6 from both sides: 10⁻⁴ = 0.1 r r = 10⁻⁴ 0.1 = 10⁻³ m = 1 mm The diameter of the marble is: d = 2r = 2 1 mm = 2 mm Stopping at the radius leads to the incorrect answer of 1 mm . Answer: 2 mm