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(A) The pressure at the bottom of a vessel due to a liquid column is given by $P = h \rho g$,where $h$ is the height of the liquid column,$\rho$ is th

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Equal in all vessels

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(A) The pressure at the bottom of a vessel due to a liquid column is given by $P = h ho g$,where $h$ is the height of the liquid column,$ho$ is the density,and $g$ is the acceleration due to gravity.Since the vessels are identical,their cross-sectional area $A$ is the same.The mass $m$ of the liquid is given by $m = ho V = ho A h$.Given that the masses are equal $(m_A = m_B = m_C = M)$,we have:$M = ho_A A h_A = ho_B A h_B = ho_C A h_C$.This implies $ho_A h_A = ho_B h_B = ho_C h_C = \frac{M}{A} = 	ext{constant}$.The pressure at the bottom is $P = ho g h = g (ho h)$.Since the product $ho h$ is constant for all three liquids,the pressure $P$ at the bottom of each vessel is the same.

Three identical vessels are filled with three liquids $A, B$,and $C$ with equal masses but having densities $\rho_A, \rho_B$,and $\rho_C$ respectively. If $\rho_A > \rho_B > \rho_C$,then the pressure at the bottom of the vessels will be:

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