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

Engineering

Physics

Buoyancy

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

more than half-filled if $ρ$ _c is more than 1.0

half-filled if $ρ$ _c is more than 0.5

less than half-filled if $ρ$ _c is less than 0.5

more than half-filled if $ρ$ _c is less than 0.5

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$mg = ρ_{w} \times \frac{V}{2} g = ρ_{w} \times V_{f} g + ρ_{c} \times V_{m} \times g$

If the vessel is half filled, the density of the material is half that of water. But if density of the material is less than half of the water, the vessel has to be more than half filled.