Water is filled up to a height h in a beaker of radius R. The density of water is $ρ$ , the surface tension of water is T and the atmospheric pressure is $P_{0}$ . Consider a vertical section ABCD of the water column through a diameter of the beaker. The force on water on one side of the section by water on the other side of this section has magnitude:

$2 P_{0} R h + π R^{2} ρ g h - 2 R T$

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$2 P_{0} R h + R ρ g h^{2} - 2 R T$

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$P_{0} π R^{2} + R ρ g h^{2} - 2 R T$

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$P_{0} π R^{2} + R ρ g h^{2} + 2 R T$

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Solution

The correct option is B
$2 P_{0} R h + R ρ g h^{2} - 2 R T$

Force, $F = \int_{0}^{h} (P_{0} + ρ g x) 2 R d x - 2 T R = 2 P_{0} R h + R ρ g h^{2} - 2 T R$

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