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 ${\rho }_c$ 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

The correct option is D less than half-filled if ${\rho }_c$ is less than $0.5$

If the cylindrical shell is half filled

$M_{shell}g=e\left(△V\right)displaced.g$

$△V=\frac{△Vshall}{2}$

$M_{shall}=\frac{e_{liquid{V}_{shell}}}{2}$

$\frac{M_{shell}}{V_{shell}}=\frac{e_{liquid}}{2}$

${\sigma }_{shell}=\frac{e_{liquid}}{2}$

$relativedensity=\frac{1}{2}$

If relative density is less than $\frac{1}{2}$ than the cylinder should be more than filled so that it is $\frac{1}{2}$ half submerged and floating more than half-filled if ${\rho }_c$ is $<\frac{1}{2}$