Equal mass of three liquids are kept in three identical cylindrical vessel  A, B  and  C . The densities are  ρA  <  ρB  <  ρc . The force on the base will be

To find the force on the base of the cylindrical vessels, we need to consider the concept of pressure. The pressure exerted by a liquid depends on its density and the height of the liquid column.

Let's assume that the height of the liquid column in each vessel is the same. Since the densities of the liquids are given as ρA < ρB < ρC, we can conclude that the liquid in vessel A is the least dense, followed by the liquid in vessel B, and finally the liquid in vessel C is the most dense.

According to Pascal's principle, the pressure at the base of each vessel will be the same, regardless of the shape or size of the vessel. Therefore, the force on the base of each vessel will be directly proportional to the pressure exerted by the liquid.

Since the height of the liquid column is the same in all three vessels, the force on the base will be directly proportional to the density of the liquid. Therefore, the force on the base will be the highest for vessel C, followed by vessel B, and the lowest for vessel A.

In conclusion, the force on the base of the cylindrical vessels will be highest for vessel C, followed by vessel B, and the lowest for vessel A.