Properties of Matter 4 Question 6
8. 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
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Answer:
Correct Answer: 8. (c)
Solution:
- Force from right hand side liquid on left hand side liquid.
(i) Due to surface tension force $=2 R T$ (towards right)
(ii) Due to liquid pressure force
$$ \begin{aligned} & =\int _{x=0}^{x=h}\left(p _0+\rho g h\right)(2 R \cdot x) d x \\ & =\left(2 p _0 R h+R \rho g h^{2}\right)(\text { towards left }) \end{aligned} $$
$\therefore$ Net force is $\left|2 p _0 R h+R \rho g h^{2}-2 R T\right|$
