physics
posted by desh .
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?

In the highly viscous "Stokes Law" Reynoldsnumber 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 steadystate limitingvelocity 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.
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