SATHEE: Properties of Matter 4 Question 6

Properties of Matter 4 Question 6

8. Water is filled up to a height $h$ in a beaker of radius $R$ as shown in the figure. The density of water is $ρ$ , the surface tension of water is $T$ and the atmospheric pressure is $p_{0}$ . Consider a vertical section $A B C D$ of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude

(2007, 3M)

(a) $| 2 p_{0} R h + π R^{2} ρ g h - 2 R T |$

(b) $| 2 p_{0} R h + R ρ g h^{2} - 2 R T |$

(c) $| p_{0} π R^{2} + R ρ g h^{2} - 2 R T |$

(d) $| p_{0} π R^{2} + R ρ g h^{2} + 2 R T |$

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Answer:

Correct Answer: 8. (b)

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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