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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?

  • physics -

    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.

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