Equilibrium of Cylinder with two liquids at either side

[ron_jay]

Homework Statement

(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:

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

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

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

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

Homework Equations

Basic Equations of hydrostatics

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?

 

[Doc Al]

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