A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in water in half-submerged state. If ρ c is the relative density of the material of t

Question

A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in water in half-submerged state. If ρ c ​ is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is

TestHub · Accepted Answer

Let V 1 ​ = total material volume of cylindrical shell V 2 ​ = total inside volume of cylindrical shell and y = fraction of V 2 ​ volume filled with water. Total weight = Upthrust (Condition of floatation) ∴ V 1 ​ ρ c ​ g + ( y V 2 ​ ) ( 1 ) g = ( 2 V 1 ​ + V 2 ​ ​ ) ( 1 ) g or y = 0.5 + ( 0.5 − ρ c ​ ) V 2 ​ V 1 ​ ​ So, if ρ c ​ < 0.5 then y > 0.5

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