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Q.

Water is filled up to a height h in a beaker of radius R as shown in the figure. The density of water is $ρ$ . Consider a vertical section ABCD 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.

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a

$| 2 ρ_{0} R h + π R^{2} ρ g h - 2 R T |$

b

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

c

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

d

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

answer is B.

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Detailed 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
$= \int_{0}^{h} (p_{0} + ρ g x) 2 R d x$
$= 2 {Rρ}_{0} h + {Rρgh}^{2} (towards left)$
Net force is $| 2 p_{0} R h + R ρ g h^{2} - 2 R T |$

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