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Q.

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

|P0πR2+Rρgh2+2RT|

b

|2P0Rh+Rρgh22RT|

c

|P0πR2+Rρgh22RT|

d

|2P0Rh+πR2ρgh2RT|

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 is

F=0h(P0+ρgx)2Rdx2RT=|2P0Rh+Rρgh22RT|

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