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Q.

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

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a

more than half-filled if ρc is less than 0.5.

b

more than half-filled if ρc is more than 1.0.

c

half-filled if ρc is more than 0.5.

d

less than half-filled if ρc is less than 0.5.

answer is A.

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Detailed Solution

Let outer volume of shell is V0 Let inner volume of shell is ViLet volume of water inside the Shell is v.⇒       1Vg + ρc(V0−Vi)g=1V02g                               Ifρc<12   ⇒    V02−VV0−Vi<12 V02−VVi2So (A)
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