# Equilibrium of Cylinder with two liquids at either side

1. Jan 1, 2008

### ron_jay

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 $$2\rho$$ and $$3\rho$$ . The height h for the equilibrium of cylinder must be:

$$a) \frac{3R}{2}$$

$$b) R \sqrt{\frac{3}{2}}$$

$$c) R \sqrt{2}$$

$$d) R \sqrt{\frac{3}{4}}$$

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?

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2. Jan 1, 2008

### Staff: Mentor

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