Two spheres of different material are falling through liquid of density 2 10^3 ~kg / m ^3 with same uniform speed. The density of sphere 1 and that of sphere 2 is 8 10^3 ~kg / m ^3 and 11 10^3 ~kg / m ^3 respectively. The ratio of their radii is (first to second sphere)

Step-by-step solution

Terminal velocity for a sphere in viscous fluid is given by Stokes' law: v_t = 2 R^2 g ( - _L) 9 . Equating terminal velocities for both spheres: R₁^2 ( ₁ - _L) = R₂^2 ( ₂ - _L) The radius ratio becomes: R₁ R₂ = ₂ - _L ₁ - _L Substituting _L = 2 10^3 kg/m^3 , ₁ = 8 10^3 kg/m^3 , and ₂ = 11 10^3 kg/m^3 : R₁ R₂ = 9 10^3 6 10^3 = 3 2 This matches option D .