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 vertic

Question

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 BC 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.

TestHub · Accepted Answer

Force from right hand side liquid on left hand side liquid. (i) Due to surface tension force = 2 RT (towards right) (ii) Due to liquid pressure force ​ = ∫ x = 0 x = h ​ ( p 0 ​ + ρ g h ) ( 2 R ⋅ x ) d x = ( 2 p 0 ​ R h + Rρ g h 2 ) (towards left) ​ ∴ Net force is ​ 2 p 0 ​ R h + Rρ g h 2 − 2 RT ​ Correct option is (b).

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