Two solid spheres, A and B, are made of the same material and are allowed to fall through a large column of a viscous liquid. The ratio of the radius of sphere A to that of sphere B is 1:2 . When both spheres have attained their respective terminal velocities, the ratio of the viscous drag force on sphere A to that on sphere B is:

Step-by-step solution

According to Stokes' law, the viscous drag force on a spherical body is: F = 6 r v The terminal velocity v_t of a sphere falling through a viscous fluid is given by: v_t = 2 9 r^2 ( - ) g This shows that the terminal velocity is directly proportional to the square of the radius ( v_t r^2 ). Substituting v_t into the drag force equation gives: F r r^2 F r^3 Alternatively, at terminal velocity, the net force is zero, meaning the viscous drag force balances the effective weight (weight minus buoyant force). Since effe