Two small solid spheres, A and B, are dropped into a tall column of a viscous fluid of density ₀ . Sphere A has a radius r and density 4 ₀ . Sphere B has a radius 2r and density 1.5 ₀ . The ratio of the terminal velocity of sphere A to that of sphere B ( v_A : v_B ) is:

Step-by-step solution

According to Stokes' law, the terminal velocity v_t of a sphere of radius R and density falling through a fluid of density is given by: v_t = 2 9 R^2 ( - ) g Thus, v_t R^2 ( - ) . For sphere A: v_A r^2 (4 ₀ - ₀) v_A 3r^2 ₀ For sphere B: v_B (2r)^2 (1.5 ₀ - ₀) v_B 4r^2 (0.5 ₀) v_B 2r^2 ₀ Taking the ratio of their terminal velocities: v_A v_B = 3r^2 ₀ 2r^2 ₀ = 3 2 Therefore, the ratio v_A : v_B is 3:2 . Answer: 3:2