Slow to rise

A uniform cylinder of length \(\ell=\SI{80}{\centi\meter}\) and radius \( r=\SI{1}{\centi\meter}\) floats on a liquid of type A and specific density \(\rho=0.9\) up to half its length. The liquid is in a long cylindrical beaker of radius \( R=\SI{4}{\centi\meter}\).

Another perfectly immiscible liquid of type B and specific density \(\sigma=0.6\) is now slowly poured all along the inner periphery of the beaker at a uniform rate of \(v=\SI[per-mode=symbol]{0.25e-4}{\meter\cubed\per\second},\) and it spreads itself uniformly over the first liquid.

Find the velocity \(v_0\) (in \(\si[per-mode=symbol]{\meter\per\second}\)) with which the cylinder rises with respect to the ground.

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