+1 vote
in Fluid Mechanics by (118k points)
A wooden cylinder of sp.gr. = 0.6 and circular in cross-section is required to float in oil(sp.gr. = 0.90). Find the L/D ratio for the cylinder to float with its longitudinal axis vertical in oil, where L is the height of cylinder and D is its diameter.

(a) L/D<9/16

(b) L/D<3/4

(c) L/D<2/3

(d) None of the mentioned

I had been asked this question during an interview.

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

1 Answer

+2 votes
by (362k points)
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Best answer
Correct option is (b) L/D<3/4

Explanation: By principle of buoyancy,

Weight of cylinder = Weight of water displaced

h=2L/3

AG=L/2

AB=L/3

BG=AG-AB=L/6

GM= Metacentric height=I/∀ – BG=3D2/32L-L/6

For stable equilibrium, GM should be positive

GM>0

i.e L/D<3/4.

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