Two solid spheres A and B are connected by a light inextensible string passing over a frictionless fixed pulley. The radius of sphere A is r and its density is 3 . The radius of sphere B is 2r and its density is . The entire system is completely immersed in a large tank of viscous liquid of density and coefficient of viscosity . The system is released from rest and eventually acquires a steady velocity v . If v = N 2

Step-by-step solution

Let us find the effective weight (weight minus buoyant force) of each sphere in the liquid. For sphere A: Volume V_A = 4 3 r^3 Weight W_A = V_A (3 ) g Buoyant force B_A = V_A g Effective downward force W'_A = W_A - B_A = V_A (2 ) g = 8 3 r^3 g For sphere B: Volume V_B = 4 3 (2r)^3 = 32 3 r^3 Weight W_B = V_B g Buoyant force B_B = V_B g Effective downward force W'_B = W_B - B_B = 0 Since W'_A > W'_B , sphere A moves downwards and sphere B moves upwards. Let the steady velocity of the system be v . At steady state, t