Properties Of Matter Ques 25
- 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
(2012)
(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
Show Answer
Answer:
Correct Answer: 25.( a )
Solution:
- 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.
In floating condition,
Total weight $=$ Upthrust
$\therefore \quad V_1 \rho_c g+\left(x V_2\right)(1) g=\left(\frac{V_1+V_2}{2}\right)(1) g$ or $ x=0.5+\left(0.5-\rho_c\right) \frac{V_1}{V_2} $
From here we can see that, $x>0.5$ if $\rho_c<0.5$
BETA
