Two solid spheres, A and B, are dropped into a large tank containing a viscous liquid of density ₀ . The radius of sphere A is R and its density is 8 ₀ . The radius of sphere B is 2R and its density is 3 ₀ . If both spheres attain their respective terminal velocities, the ratio of the terminal velocity of sphere A to that of sphere B ( v_A : v_B ) is

Step-by-step solution

The terminal velocity v_T of a sphere of radius r and density _ sphere falling through a liquid of density _ liquid and viscosity is given by: v_T = 2 9 r^2 ( _ sphere - _ liquid ) g Thus, the terminal velocity is proportional to r^2 ( _ sphere - _ liquid ) . For sphere A: v_A R^2 (8 ₀ - ₀) = 7R^2 ₀ For sphere B: v_B (2R)^2 (3 ₀ - ₀) = 4R^2 (2 ₀) = 8R^2 ₀ Taking the ratio of their terminal velocities: v_A v_B = 7R^2 ₀ 8R^2 ₀ = 7 8 The ratio v_A : v_B is 7 : 8 . Answer: 7 : 8