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Directions : In the following question more than one of the answers given may be correct. Select the correct answer and mark it according to the code:

The vessel shown in figure has two sections of areas of cross-section\[{{A}_{1}}\]and\[{{A}_{2}}\]. A liquid of density p fills both the sections, up to height h in each neglecting atmospheric pressure. (1) The pressure at the base of the vessel is\[2h\rho g\] (2) The force exerted by the liquid on the base of vessel is\[2h\rho g{{A}_{2}}\] (3) The walls of the vessel at the level\[X\]exert a force\[h\rho g({{A}_{2}}-{{A}_{1}})\]downwards on the liquid (4) The weight of the liquid in vessel is equal to\[2h\rho g{{A}_{2}}\]

A)  1, 2 and 3 are correct

B)  1 and 2 are correct

C)   2 and 4 are correct

D)  1 and 3 are correct

Correct Answer: A

Solution :

                 The liquid at one level exerts pressure equally in all directions. The height of liquid column\[=2h\] So, pressure at the base of the vessel is\[=2h\rho g\] The force exerted by the liquid on the base of vessel\[=Pressure\times base\text{ }area\] \[=2h\rho g\times {{A}_{2}}\] Down force on wall of vessel at level\[X\]is due to liquid pressure of height h on area\[{{A}_{2}}\] \[=h\rho g{{A}_{2}}\] Upward force on the wall of vessel at level X is due to liquid pressure of height h on area\[{{A}_{1}}\] \[=h\rho g{{A}_{1}}\] \[\therefore \] Net downward force on wall of vessel at level X                 \[=h\rho g{{A}_{2}}-h\rho g{{A}_{1}}\]  \[=h\rho g({{A}_{2}}-{{A}_{1}})\] The weight of the liquid in vessel              \[={{A}_{1}}h\rho g+{{A}_{2}}h\rho g\] Hence, option  is correct.