Two steel spheres, A and B, are falling through the same viscous oil. The ratio of the radius of sphere A to that of sphere B is 2:3 . If the ratio of their instantaneous velocities is 3:4 , what is the ratio of the viscous drag forces acting on sphere A and sphere B?

Step-by-step solution

According to Stokes' law, the viscous drag force F_v on a sphere of radius r moving with velocity v in a fluid of viscosity is given by: F_v = 6 r v Since both spheres are falling through the same oil, is constant. Therefore, the viscous drag force is directly proportional to the product of radius and velocity: F_v r v The ratio of the viscous drag forces is: F_A F_B = ( r_A r_B ) ( v_A v_B ) Substituting the given ratios: F_A F_B = ( 2 3 ) ( 3 4 ) = 2 4 = 1 2 Thus, the ratio of the viscous drag forces is 1:2 . Squ