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 $\mathrm{1.0.}$
• 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