Question

A solid cylinder of diameter 5.0 m has a height of 6.0 m. Find the meta-centric height of the cylinder if the specific gravity of the material of cylinder 0.45 and it is floating in water with its axis vertical. State whether the equilibrium is stable or unstable.

(a) -0.29 m

(b) -0.61 m

(c) -1.16 m

(d) 0.14 m

This question was addressed to me during an internship interview.

The origin of the question is Conditions of Equilibrium of a Floating and Submerged Bodies in portion Buoyancy and Floatation of Fluid Mechanics

Answer 1

Right answer is (b) -0.61 m

Easiest explanation: BG=Centre of pontoon – Centre of immersed portion=0.3-0.45*0.3=1.65

                     Metacentric height=I/∀ -BG

                     I=π*r⁴=π*2.5⁴

                     ∀=π*r*r*h=π*2.5*2.5*6

                     Metacentric height=-0.61.