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 $\rho_{ C }$ is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is

• A. more than half-filled if $\rho_{c}$ is less than $0.5$
• B. more than half-filled if $\rho_{ C }$ is more than $1.0 .$
• C. half-filled if $\rho_{c}$ is more than $0.5$.
• D. less than half-filled if $\rho_{ C }$ is less than $0.5$.

Answer 1

Answer: (A)

$\frac{ V _{ m }+ V _{ a }+ V _{ x }}{2} \rho_{ w } g = V _{ m } \rho_{ c } \rho_{ w } g + V _{ v } \rho_{ w } g$
$ V _{ w }= V _{ m }\left(1-2 \rho_{ c }\right)+ V _{ a } $
if $ \rho_{ c }>\frac{1}{2} \Rightarrow V _{ w }< V _{ a }$
if $ \rho_{c}<\frac{1}{2} \Rightarrow V _{ x }> V _{2}$
where, $V_{w}=$ volume occupied by water in the shell
$V _{a}=$ volume occupied by air in the shell
$V_m =$ volume of the material in the shell