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 _c is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is

JEE Advanced 2012 Physics 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 is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is

(A)more than half-filled if is less than 0.5.Correct
(B)more than half-filled if is more than 1.0.
(C)half-filled if is more than 0.5.
(D)less than half-filled if is less than 0.5.

Answer: (A)

Solution

Let the internal volume be V, the volume of the shell material , and let a fraction f of V be filled with water. Floating half submerged, the shell displaces half its total external volume: buoyancy . Weight cV_s$ +

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Question ID VK-026066