Irodov Problem 1.339

Let the density of steel be and that of olive oil be and let the viscosity of olive oil be. Suppose that at some instant the velocity of the sphere is v.

As the sphere sinks, there are three forces acting on it, i) the force of gravity responsible for sinking it given by ii) the buoyant force offered by the fluid given by and iii) the viscous force offered by the fluid .

The mass of the sphere is given by and so from Newton's first law we have,
























From (2) it is clear that the steady state velocity will be . The velocity v will be off by from the steady state velocity by fraction n when,







From (1) we have,