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(C) The pressure $P$ exerted by a liquid column of height $h$ and density $\rho$ on the base of a vessel is given by $P = \rho g h$.The force $F$ exer

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The same in all vessels

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(C) The pressure $P$ exerted by a liquid column of height $h$ and density $ho$ on the base of a vessel is given by $P = ho g h$.The force $F$ exerted on the base of area $A_{base}$ is $F = P 	imes A_{base}$.Since the vessel is cubical,the volume $V$ of the liquid is $V = A_{base} 	imes h$. Thus,$h = \frac{V}{A_{base}}$.Substituting this into the pressure formula:$P = ho g \left(\frac{V}{A_{base}}ight) = \left(\frac{ho V}{A_{base}}ight) g$.Since mass $m = ho V$,we have $P = \frac{mg}{A_{base}}$.Therefore,the force $F$ is:$F = P 	imes A_{base} = \left(\frac{mg}{A_{base}}ight) 	imes A_{base} = mg$.Since the masses $m$ of the liquids in all three vessels are equal and $g$ is constant,the force exerted on the base of each vessel is $F = mg$.Thus,the force is the same in all vessels.

Three liquids of equal masses are taken in three identical cubical vessels $A, B$ and $C$. Their densities are $\rho_{A}, \rho_{B}$ and $\rho_{C}$. The force exerted by the liquid on the base of the cubical vessel is

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