SATHEE: Properties of Matter 4 Question 6

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 $ρ_{c}$ 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 $ρ_{c}$ is less than 0.5

(b) more than half-filled if $ρ_{c}$ is more than 1.0

(d) less than half-filled if $ρ_{c}$ 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

$\begin{aligned} = \int_{x = 0}^{x = h} (p_{0} + ρ g h) (2 R \cdot x) d x \\ = (2 p_{0} R h + R ρ g h^{2}) (towards left) \end{aligned}$

$∴$ Net force is $| 2 p_{0} R h + R ρ g h^{2} - 2 R T |$

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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 ρc is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is

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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 $ρ_{c}$ is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is