# Fluid Mechanics-3

Classical Mechanics Level 5

A uniform cylinder of a light material of length $$l=0.8m$$ and radius of cross-section $$r=0.01m$$ floats on a liquid of specific density $$\rho=0.9$$ upto half its length. The container of the liquid is a long cylindrical beaker of radius $$R=0.04m$$. Another perfectly immiscible liquid of specific density $$\sigma=0.6$$ is now slowly poured all along the inner periphery of the beaker at a uniform rate of $$v=0.25\times { 10 }^{ -4 }{ m }^{ 3 }/s$$ and it spreads itself uniformly over the first liquid. Find the velocity with which the cylinder will rise or sink in the liquid.

It can be expressed as $$\frac { 1 }{ k\pi }$$, then find the value of $$k$$.

$$\bullet$$ Please upload a nice solution.

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