+1 vote
in Fluid Mechanics by (118k points)
A cylinder(uniform density distribution) of  radius 3.0 m has a height of 9.0 m. The specific gravity of the material of cylinder 0.85 and it is floating in water with its axis vertical. State whether the equilibrium is stable or unstable.

(a) Stable

(b) Unstable

(c) Insufficient Data

(d) None of the mentioned

The question was asked in an international level competition.

This intriguing question originated from Conditions of Equilibrium of a Floating and Submerged Bodies in division Buoyancy and Floatation of Fluid Mechanics

1 Answer

+2 votes
by (362k points)
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Best answer
Correct choice is (a) Stable

To explain I would say: BG=Centre of pontoon – Centre of immersed portion=0.3-0.45*0.3=1.65

                     Metacentric height=I/∀ -BG

                     I=π*r⁴=π*3⁴

                     ∀=π*r*r*h=π*3*3*9

                     Metacentric height=0.325.

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