A bottle is kept on the ground as shown in the figure. The bottle can be modelled as having two cylindrical zones. The lower zone of the bottle has a cross-sectional radius of R 2 and is filled with

Question

A bottle is kept on the ground as shown in the figure. The bottle can be modelled as having two cylindrical zones. The lower zone of the bottle has a cross-sectional radius of $R 2$ and is filled with honey of density $2 ρ$ . The upper zone of the bottle is filled with the water of density $ρ$ and has a cross-sectional radius R. The height of the lower zone is H while that of the upper zone is 2H . If now the honey and the water parts are mixed together to form a homogeneous solution. (Assume that total volume does not change)

TestHub · Accepted Answer

Initial pressure at bottom: P i ​ = ρ g ( 2 H ) + 2 ρ g H = 4 ρ g H Mean density after mixing: ρ m ​ = A ( 2 H ) + 2 A H ρ A ( 2 H ) + 2 ρ ( 2 A ) H ​ = 2 3 ρ ​ Final pressure at bottom: P f ​ = 2 3 ρ ​ g ( 3 H ) = 2 9 ​ ρ g H So pressure rises from 4 ρ g H to 2 9 ​ ρ g H : B and C are correct.

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