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Homework Help: Equilibrium of Cylinder with two liquids at either side

  1. Jan 1, 2008 #1
    1. The problem statement, all variables and given/known data

    (Please refer to the attachment given)

    In the figure shown, the heavy cylinder (radius R) resting on a smooth surface separates two liquids of densities [tex] 2\rho [/tex] and [tex]3\rho[/tex] . The height h for the equilibrium of cylinder must be:

    [tex] a) \frac{3R}{2} [/tex]

    [tex] b) R \sqrt{\frac{3}{2}} [/tex]

    [tex] c) R \sqrt{2} [/tex]

    [tex] d) R \sqrt{\frac{3}{4}} [/tex]

    2. Relevant equations

    Basic Equations of hydrostatics

    3. The attempt at a solution

    This Problem is a little confusing. I think we have to consider the components of the pressures at various points on the cylinder, but I am not too sure how.Besides the above question, how would the cylinder move in the given state of inequilibrium?
     

    Attached Files:

  2. jcsd
  3. Jan 1, 2008 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Hint: Consider imaginary vertical walls just touching both sides of the cylinder. Now examine the forces acting on those walls.
     
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