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)

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TestHub · Accepted Answer

Initial bottom pressure: p i ​ = ρ g ( 2 H ) + 2 ρ g ( H ) = 4 ρ g H . Honey volume is 2 A H and water volume is 2 A H , so mixture density is 3 ρ /2 . Total volume 4 A H occupies final height 3 H across the two zones. Final bottom pressure: p f ​ = ( 3 ρ /2 ) g ( 3 H ) = 9 ρ g H /2 . Pressure rises by ρ g H /2 ; total weight and ground reaction stay unchanged. Answers: B, C.

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