Momentum and CollisionHard

Question

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

Options

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.

Solution

ρw g = Vmρcρwg + Vwρwg
Vw = Vm(1- 2ρc) + Va
if ρc > ⇒ Vw < Va
if ρc < ⇒ Vw > Va,
where, Vw = volume occupied by water in the shell
            Va = volume occupied by air in the shell
            Vm = volume of the material in the shel

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