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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 $ρ$ , the surface tension of water is T and the atmospheric pressure is P₀. 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

$|2 p_{0} Rh + {πR}^{2} ρgh - 2 RT|$

b

$|2 P_{0} Rh + {Rρgh}^{2} - 2 RT|$

c

$|P_{0} {πR}^{2} + {Rρgh}^{2} - 2 RT|$

d

$|P_{0} {πR}^{2} + {Rρgh}^{2} + 2 RT|$

answer is B.

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Detailed Solution

Question Image

$F = \int_{o}^{h} (P_{0} + ρgx) 2 R dx - 2 RT = 2 P_{0} Rh + {Rρgh}^{2} - 2 RT$

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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 P0. 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: