# 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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