# 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 \( k \).

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