Three identical cylindrical vessels A, B, and C contain equal...

The force exerted by a liquid on the base of a cylindrical vessel is given by $F = P \times A$, where $P$ is the pressure at the base and $A$ is the area of the base.

The pressure at the base is $P = \rho g h$, where $\rho$ is the density of the liquid and $h$ is the height of the liquid column.

Substituting $P$ into the force equation gives $F = \rho g h A$.

The volume of the liquid is $V = h A$, and the mass of the liquid is $m = \rho V = \rho h A$.

Therefore, the force on the base can be written as $F = m g$.

Since the three vessels contain equal masses of the liquids, the force exerted on the base will be equal to the weight of the liquid, which is the same in all the vessels.