Two small metal spheres of densities in the ratio 3:2 and diameters in the ratio 1:2 are released from rest in two vertical liquid columns of coeff. of viscosities in the ratio 4:3. When the viscous force on both of them is same, what will be the ratio of their instantaneous velocities?

Answer 1

In the highly viscous "Stokes Law" Reynolds-number region (Re < 0.1), the viscous force is proportional to velocity*diameter*viscosity.
It does not depend upon density.

If the viscous forces are equal instantaneously,
V2/V1 = (D1/D2)*(Visc1/Visc2)
= (1/2)(4/3) = 2/3

This question is fundamentally flawed in my opinion, for this reason. In the steady-state limiting-velocity regime, the viscous forces cannot be equal in this case, since the force ratio must equal the weight (and mass) ratio, which is not 1 in this case.