[UPSC CSE 1991] Mechanics of Continuous media (Q302, 20M)

A sphere of radius a_1 made of a material of density p_1 falls through a fluid with terminal velocity v_1. Another sphere of radius a_2 made of a material of density p_2 falls through the same liquid with terminal velocity v_2. Assuming that the viscous dreg for these particles is given by \pi \eta a v. show that the viscosity of the fluid is given by \frac{2 g a_1^2 a_2^2 (p_2 - p_1)}{9 (a_1^2 v_2 - a_2^2 v_1)}