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A thin uniform cylindrical shell, closed at both ends, is
\( \mathrm{P} \) partially filled with water. It is floating vertically in water in

W half-submerged state. If \( \rho_{c} \) is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is
[IIT JEE 2012]
(a) More than half filled if \( \rho_{c} \) is less than 0.5
(b) More than half filled if \( \rho_{c} \) is less than 1.0
(c) Half filled if \( \rho_{c} \) is less than 0.5
(d) Less than half filled if \( \rho_{c} \) is less than 0.5
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