Water is filled up to a height h in a breaker of radiusR . The density of water isρ , the surface tension of water is T and the atmospheric pressure isP0 . 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
|2P0Rh+πR2ρgh−2RT|
b
|2P0Rh+Rρgh2−2RT|
c
|P0πR2+Rρgh2−2RT|
d
|P0πR2+Rρgh2+2RT|
answer is B.
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Detailed Solution
Consider water on one side of the vertical section ABCD as the system.Note that this is the half-cylinder. Draw the forces on this half-cylinder by another half-cylinder. At a depth below x from the top surface consider a strip of widthdx . Force on this strip is(P0+ρgx)(2Rdx) . Total force on one half-cylinder by the other half-cylinder isF=∫0h(P0+ρgx)2Rdx−2RT=|2P0Rh+Rρgh2−2RT|