Discussion Forum



1)

A thin uniform cylindrical shell closed at both ends, is partially filled with water. It is floating vertically in water in a 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:

Option A

Explanation:

Let $V_{1}$= total material volume of shell

$V_{2}$= total inside volume of shell and

x = fraction of $V_{2}$ volume filled with water.

ln floating condition,
Total weight = Upthrust

 $\therefore$     $V_{1} \rho_{c} g+(xV_{2})(1)g=\left(\frac{V_{1}+V_{2}}{2}\right)(1)g$

 or $  x=0.5+(0.5+\rho_{c}) \frac{V_{1}}{V_{2}}$

from here we can see that 

      $x>0.5$ if $\rho_{c} <0.5$